Receiving Helpdesk

what shapes are equiangular and equilateral

by Prof. Creola Kessler DDS Published 3 years ago Updated 2 years ago

  • All the angles of an equilateral triangle are equal to 60°.
  • Equiangular shapes are shapes in which all the interior angles are equal.
  • A square is a special case of an equilateral quadrilateral in which all the angles and sides are equal.
  • If a rhombus is equiangular, it is a square.

Equilateral and Equiangular Three-Sided Polygons (triangles)
Because of how rigid and structured a triangle is, all equilateral triangles are also equiangular. Every equilateral triangle has three 60-degree angles inside the triangle and three 120-degree angles outside the triangle.
Nov 30, 2021

Full Answer

What shapes are equilateral?

The tessellated structures can be constructed from small solar-cell units that come in a range of shapes such as rectangles, equilateral triangles and right-angled triangles. An elastic material such as silicone rubber or a metal mesh should be used as the ...

Are equiangular triangles always equilateral?

In an equiangular triangle, all the angles are equal—each one measures 60 degrees. An equiangular triangle is a kind of acute triangle, and is always equilateral. In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. An acute triangle may be equilateral, isosceles, or scalene.

What does equiangular mean?

Equiangular means a polygon all of whose angles are equal to each other, equilateral means the sides are all equal. A rectangle is equiangular , a rhombus is equilateral . A square is both.

Is a rectangle equiangular?

In Euclidean geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all angles are equal (360°/4 = 90°); or a parallelogram with a right angle. What is a rectangular short answer? A rectangle is a four-sided shape with all angles at ninety degrees.

Which shape is both equilateral and equiangular?

When a polygon is both equilateral and equiangular, it is called a regular polygon. A square is an example of a regular polygon.

What quadrilaterals are equiangular and equilateral?

If a quadrilateral is equilateral and equiangular, it's a square. If a rhombus is equiangular, it's a square. If a rectangle is equilateral, it's a square.

What are equiangular shapes?

In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon.

Are rectangles equilateral and equiangular?

A rectangle is equilateral but not equiangular. Convex polygons have no portions of their diagonals in their exteriors. Equilateral triangles are always equiangular.

What is quadrilaterals shapes?

A quadrilateral is a 4 sided closed figure. These figures are quadrilaterals: A shape with four sides. The shape has one set of parallel sides and does not have any right angles.

What does equilateral mean in geometry?

equilateral triangleDefinition of equilateral 1 : having all sides equal an equilateral triangle an equilateral polygon — see triangle illustration. 2 : having all the faces equal an equilateral polyhedron.

Are hexagons equilateral?

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). times the apothem (radius of the inscribed circle). All internal angles are 120 degrees.

Is equiangular a triangle?

Equiangular triangles are a type of triangles with the angles and sides equal to each other. We can say that an equiangular triangle is also called an equilateral triangle. It is a regular polygon with three equal sides with angles of the same measure....Equiangular Triangles.1.What are Equiangular Triangles?6.FAQs on Equiangular Triangles4 more rows

Are all equiangular hexagons similar?

Not all hexagons are the same shape. All hexagons are not similar. A rectangle is a parallelogram with one right angle. The length and width can vary.Jul 20, 2015

Is an equiangular quadrilateral a rectangle?

An equiangular quadrilateral, i.e. the one with all angles equal is a rectangle. All angles of a rectangle equal 90°. An equilateral quadrilateral, i.e. the one with all sides equal, is a rhombus.

Is square equiangular?

Square: A square is a two-dimensional plane figure with four equal sides, four interior right angles, and four corners. In other words, a square is a quadrilateral or a 4-sided polygon. All the angles are of equal measure, therefore it is considered as an equiangular quadrilateral.

What shape is equilateral but not equiangular?

In geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it doesn't need to be equiangular (doesn't need to have all angles equal), but if it does then it is a regular polygon.

Why are all equilateral triangles equiangular?

Because of how rigid and structured a triangle is , all equilateral triangles are also equiangular. Every equilateral triangle has three 60-degree angles inside the triangle and three 120-degree angles outside the triangle. Equilateral and Equiangular Four-Sided Polygons (quadrilaterals)

What is an equiangular polygon?

An equiangular polygon (from Latin aequi meaning ''equal'' and angularis meaning ''having corners or sides'' ) is a figure with straight sides, like other polygons, but in this figure every internal angle has the same measure. For example, rooms in a typical house usually have square corners; that is, the measure of every corner is 90 degrees.

What does an ice cube look like?

Imagine an ice cube—a perfectly square frozen block of ice, sitting on the desk. If you look at it, straight on from the top, you'll see that it looks like a square. Its sides all measure the same length. Its edges all come together to make perfectly square corners, 90 degrees, just like the corners of a typical house. The top of that ice cube—if it's a perfectly square one—forms one kind of equilateral and equiangular polygon.

What is a quadrilateral with 4 sides called?

Equilateral quadrilaterals (or four-sided polygons) all have four equal sides, regardless of the angles between the sides. Also called a rhombus, these figures are either a square, in which case all four angles also are equal, or a non-square rhombus. Other Equiangular and Equilateral Polygons.

What does it mean when a polygon is concave?

If it's concave, that means that at least one angle is more than 180 degrees (meaning more than a straight line) and looks bent backward like the one in the pentagon with the red angle. ...

How many sides does a polygon have?

As we learned, polygons are geometric figures with straight sides. They will have at least three sides, and may have many more. Remember: ''equi'' means equal, ''lateral'' means sides, and ''angular'' means angles. Therefore, if all of the sides of the polygon are the same length, the polygon is said to be equilateral, ...

Which polygon has more than 4 sides?

Other Equiangular and Equilateral Polygons. Equilateral polygons with more than four sides are also usually equiangular. If the sides are all the same length, then they also have the same angle measurement.

Equilateral Polygon Definition

Equilateral polygon definition: An equilateral polygon is one having sides of equal length. An equilateral triangle, for example, has three sides of the same length, while a square has four. The term equilateral is derived from the Latin words equi -, or same, and latus, or side.

Equiangular Polygon Definition

Equiangular polygon definition: An equiangular polygon is one having the same, or congruent, interior angles, although it may also be said that, by reciprocity, the exterior angles may also all be the same. An equiangular triangle may have three 60-degree inner angles, but it is also true that it has six 120-degree exterior angles.

Equiangular Triangle Definition

Equiangular Triangle Definition: An equiangular triangle is one in which the three interior angles all measure 60 degrees. The three interior angles must add up to 180 degrees.

What does "equilateral" mean in math?

(geometry) Of a polygon, having all interior angles equal. This is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square.

Is a rectangle equiangular or equilateral?

is that equiangular is (geometry) of a polygon, having all interior angles equal this is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square while equilateral is (geometry) referring to a polygon all of whose sides are of equal length not necessarily a regular polygon since the angles can still differ (a regular polygon would also be equiangular).

What is an equiangular shape?

Equiangular shapes are shapes in which all the interior angles are equal. A square is a special case of an equilateral quadrilateral in which all the angles and sides are equal. If a rhombus is equiangular, it is a square.

How many sides does an equilateral triangle have?

An equilateral triangle is a regular polygon with 3 equal sides. The figure given above shows that triangle PQR is an equilateral triangle. Hence, the equal sides can be written as: PQ = QR= RP. It should be noted that all the angles of this triangle are also equal. ∠PQR = ∠QRP = ∠RPQ = 60°.

What is a triangle made of?

We know that polygons are shapes that are made up of straight line segments, and a triangle is a polygon with the minimum number of sides. Now, if the side lengths of the polygons are equal, we call them equilateral shapes. Let's explore these equilateral shapes and their properties in detail now.

What is the meaning of equilateral?

Equilateral is defined as any shape which has all its sides equal.

Is a square a quadrilateral?

A square is a special case of equilateral quadrilateral in which all the four angles are equal. Thus, it can be said that if a quadrilateral is equilateral and equiangular, it is a square. Square ABCD is an equilateral quadrilateral with all the four angles equal to 90°.

Is a rhombus an equilateral quadrilateral?

Equilateral Quadrilateral. An equilateral quadrilateral is a polygon with 4 equal sides and it is called a rhombus. The figure given below shows that rhombus PQRS is an equilateral quadrilateral. We cannot say that all the angles of an equilateral quadrilateral are equal. A square is a special case of equilateral quadrilateral in which all ...

Is a right angled triangle equilateral?

No, right triangles are not equilateral. In a right-angled triangle, the length of the hypotenuse is always greater than the other two sides whereas in an equilateral triangle all the sides are equal. So, a right-angled triangle does not follow the rules for an equilateral triangle.

image
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version2.46sRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[06:46:27] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[06:46:27] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[06:46:27] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[06:46:27] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[06:46:27] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[06:46:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[06:46:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[06:46:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[06:46:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • Booting (12.33ms)
  • Application (2.45s)
  • 1 x Application (99.48%)
    2.45s
    1 x Booting (0.5%)
    12.33ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed2.43s
    • select * from `posts` where `published_at` <= '2025-06-16 06:46:27' and `slug` = 'what-shapes-are-equiangular-and-equilateral' and `posts`.`deleted_at` is null limit 1
      1.73ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-16 06:46:27
      • 1. what-shapes-are-equiangular-and-equilateral
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 138871 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      8.26msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 138871
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      680μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      420μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      200μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      2.42s/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 30562 limit 1
      860μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 30562
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        FjHYqtdVn8YL55kkcm1QgglSyQwOeUGIwsPDqA8g
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-shapes-are-equiangular-and-equilateral"...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /what-shapes-are-equiangular-and-equilateral
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=ab5d89f83a2cef8d.1750036580.; _pk_ses.64.7c30=1; _pk_id.63.7c30=6bc188215d0677c9.1750036588.; _pk_ses.63.7c30=1; XSRF-TOKEN=eyJpdiI6Ilh4Z2d6TktRM0xxd25mUDNTMnRPNGc9PSIsInZhbHVlIjoiQTVjaHVHdGJlbEVMaEpzNENtU1hra1NxQ1RtazErcHF4Wk81b2l4SVBFRE5JdFFlUzloTFlnSEFFaG11NkN2NWV6L1NmdmFrYTRGMllXS21ZZ3dITnB0ZnlxRlZCaGRnbUVGWXJSaUsxcURJTGdKdGY1akk2YXB3Z2ZPakZvMFkiLCJtYWMiOiIxYTRiZjYxNmRkZTMyN2M4ODY3MmQ1ZjA4ODIxYWMxOTJiMTBmZWY3OTNiNjlhYmY0MmRiN2RjZjIxMTgxNmY4IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IlFYRjI1TzZic3lSSE9yUDhYUWRpTXc9PSIsInZhbHVlIjoiNnJiSXFoL09mMWNFL1Q4YW5DVjc1R1phWTZMOHdHWEk4YXpUeXhwYjE1clhxTWRtMElvaUlYbmgwWWJ0RVBUOWRPRXowV3pSV3YxQllvdVg5U201NnJwTVBDNVBibjVWVVF0MmFnZWcxV2Z6UmNwS2VYSVdFeXlPZW1vZWt6VDciLCJtYWMiOiJkYzVjODhiZDQ2MTZlOTNlMTk3YjUwNGU5NjgzMzUzNWE2ZDNhYTU5NTI0OTIwMDcyYTFmYzBhZmU4MjE2NjUzIiwidGFnIjoiIn0%3D_pk_id.64.7c30=ab5d89f83a2cef8d.1750036580.; _pk_ses.64.7c30=1; _pk_id.63.7c30=6bc188215d0677c9.1750036588.; _pk_ses.63.7c30=1; XSRF-TOKEN=eyJpdiI6Ilh4Z2d6TktRM" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.208" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "95067642bb05f4a2-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.208, 172.69.58.142" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/what-shapes-are-equiangular-and-equilateral" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/what-shapes-are-equiangular-and-equilateral" "REMOTE_PORT" => "55678" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.69.58.142" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=ab5d89f83a2cef8d.1750036580.; _pk_ses.64.7c30=1; _pk_id.63.7c30=6bc188215d0677c9.1750036588.; _pk_ses.63.7c30=1; XSRF-TOKEN=eyJpdiI6Ilh4Z2d6TktRM0xxd25mUDNTMnRPNGc9PSIsInZhbHVlIjoiQTVjaHVHdGJlbEVMaEpzNENtU1hra1NxQ1RtazErcHF4Wk81b2l4SVBFRE5JdFFlUzloTFlnSEFFaG11NkN2NWV6L1NmdmFrYTRGMllXS21ZZ3dITnB0ZnlxRlZCaGRnbUVGWXJSaUsxcURJTGdKdGY1akk2YXB3Z2ZPakZvMFkiLCJtYWMiOiIxYTRiZjYxNmRkZTMyN2M4ODY3MmQ1ZjA4ODIxYWMxOTJiMTBmZWY3OTNiNjlhYmY0MmRiN2RjZjIxMTgxNmY4IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IlFYRjI1TzZic3lSSE9yUDhYUWRpTXc9PSIsInZhbHVlIjoiNnJiSXFoL09mMWNFL1Q4YW5DVjc1R1phWTZMOHdHWEk4YXpUeXhwYjE1clhxTWRtMElvaUlYbmgwWWJ0RVBUOWRPRXowV3pSV3YxQllvdVg5U201NnJwTVBDNVBibjVWVVF0MmFnZWcxV2Z6UmNwS2VYSVdFeXlPZW1vZWt6VDciLCJtYWMiOiJkYzVjODhiZDQ2MTZlOTNlMTk3YjUwNGU5NjgzMzUzNWE2ZDNhYTU5NTI0OTIwMDcyYTFmYzBhZmU4MjE2NjUzIiwidGFnIjoiIn0%3D_pk_id.64.7c30=ab5d89f83a2cef8d.1750036580.; _pk_ses.64.7c30=1; _pk_id.63.7c30=6bc188215d0677c9.1750036588.; _pk_ses.63.7c30=1; XSRF-TOKEN=eyJpdiI6Ilh4Z2d6TktRM" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.208" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "95067642bb05f4a2-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.208, 172.69.58.142" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1750036587.9739 "REQUEST_TIME" => 1750036587 ]
        request_cookies
        0 of 0
        array:6 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "_pk_id_63_7c30" => null "_pk_ses_63_7c30" => null "XSRF-TOKEN" => "FjHYqtdVn8YL55kkcm1QgglSyQwOeUGIwsPDqA8g" "askhelpdesk_session" => "5jdjgIb3nkHsPoHuJlCtApGK3H2KagUwRsf2F2cu" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Mon, 16 Jun 2025 01:16:28 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ikp2clRiTkIwRzBIMm1vK2lPaENDYmc9PSIsInZhbHVlIjoiaHArcTBOL2xOMHlqaS9oR0xkK3JFVlNtSEJSdzc2K1lzeGtueTJ1Qy9vM1Nydm53ZVBWRHMrbG0vdk1mOFlEdzBXWk4yc3dFWjlabTNLTVRTZTRQTk5OZGlSMklsRHA1Rm9RdFBxQ1lkWWZWN1pIcjIweC9pOTRyRHNWQUlhbzEiLCJtYWMiOiI2ZWYzMzMzZjcwNjU1YjY5MjMzYTkwODc1Yzg4OGI2YmY3NzMxYTJiNThiZWY2MTA3MDA3ODBlN2JmMTM1NDRiIiwidGFnIjoiIn0%3D; expires=Mon, 16-Jun-2025 03:16:30 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6Ikp2clRiTkIwRzBIMm1vK2lPaENDYmc9PSIsInZhbHVlIjoiaHArcTBOL2xOMHlqaS9oR0xkK3JFVlNtSEJSdzc2K1lzeGtueTJ1Qy9vM1Nydm53ZVBWRHMrbG0vdk1mOFlEdzBXWk4yc" 1 => "askhelpdesk_session=eyJpdiI6IkhjZTZITG14RTZUZzNnQ0haSnoxbVE9PSIsInZhbHVlIjoiNW9mNjdlS0pVejRhcU4wTGJJcVhhYWM4WnNKRC9IUEkwd1JTNlgxUitkalgyMlp1RTl4bzNwbFNDL3ZDSmtrZG9mZGxGTWhZZU4vdnhHdEtsbzJ0RlcyNVJsakI4SFBoOW4xeGdMODJPTFpOL0p1ODJGbEdsQTl2TnJWK0cyQWEiLCJtYWMiOiJmODJmMjA5MDliM2EwODc0ZmE1NmY2MDBlNjJlYzQzZDg5MjU0M2U4ZTNmZjBkOWZmZWM1OGIzZDYyNDE5YzZlIiwidGFnIjoiIn0%3D; expires=Mon, 16-Jun-2025 03:16:30 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6IkhjZTZITG14RTZUZzNnQ0haSnoxbVE9PSIsInZhbHVlIjoiNW9mNjdlS0pVejRhcU4wTGJJcVhhYWM4WnNKRC9IUEkwd1JTNlgxUitkalgyMlp1RTl4bzNwbFNDL3ZDSmtr" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ikp2clRiTkIwRzBIMm1vK2lPaENDYmc9PSIsInZhbHVlIjoiaHArcTBOL2xOMHlqaS9oR0xkK3JFVlNtSEJSdzc2K1lzeGtueTJ1Qy9vM1Nydm53ZVBWRHMrbG0vdk1mOFlEdzBXWk4yc3dFWjlabTNLTVRTZTRQTk5OZGlSMklsRHA1Rm9RdFBxQ1lkWWZWN1pIcjIweC9pOTRyRHNWQUlhbzEiLCJtYWMiOiI2ZWYzMzMzZjcwNjU1YjY5MjMzYTkwODc1Yzg4OGI2YmY3NzMxYTJiNThiZWY2MTA3MDA3ODBlN2JmMTM1NDRiIiwidGFnIjoiIn0%3D; expires=Mon, 16-Jun-2025 03:16:30 GMT; path=/XSRF-TOKEN=eyJpdiI6Ikp2clRiTkIwRzBIMm1vK2lPaENDYmc9PSIsInZhbHVlIjoiaHArcTBOL2xOMHlqaS9oR0xkK3JFVlNtSEJSdzc2K1lzeGtueTJ1Qy9vM1Nydm53ZVBWRHMrbG0vdk1mOFlEdzBXWk4yc" 1 => "askhelpdesk_session=eyJpdiI6IkhjZTZITG14RTZUZzNnQ0haSnoxbVE9PSIsInZhbHVlIjoiNW9mNjdlS0pVejRhcU4wTGJJcVhhYWM4WnNKRC9IUEkwd1JTNlgxUitkalgyMlp1RTl4bzNwbFNDL3ZDSmtrZG9mZGxGTWhZZU4vdnhHdEtsbzJ0RlcyNVJsakI4SFBoOW4xeGdMODJPTFpOL0p1ODJGbEdsQTl2TnJWK0cyQWEiLCJtYWMiOiJmODJmMjA5MDliM2EwODc0ZmE1NmY2MDBlNjJlYzQzZDg5MjU0M2U4ZTNmZjBkOWZmZWM1OGIzZDYyNDE5YzZlIiwidGFnIjoiIn0%3D; expires=Mon, 16-Jun-2025 03:16:30 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6IkhjZTZITG14RTZUZzNnQ0haSnoxbVE9PSIsInZhbHVlIjoiNW9mNjdlS0pVejRhcU4wTGJJcVhhYWM4WnNKRC9IUEkwd1JTNlgxUitkalgyMlp1RTl4bzNwbFNDL3ZDSmtr" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "FjHYqtdVn8YL55kkcm1QgglSyQwOeUGIwsPDqA8g" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-shapes-are-equiangular-and-equilateral" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]