what theorem or postulate is used to prove abcd is a parallelogram

by Mr. Demond Kling Jr. Published 3 years ago Updated 2 years ago

Theorem 1: A diagonal of a parallelogram divides it into two congruent triangles. Given: A parallelogram (ABCD

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) and diagonal (AC) divide it into two triangles (△ABC) and (△CDA.) To prove: (△ABC≅△CDA)

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Full Answer

What two numbers prove that ABCD is a parallelogram?

[Expert Answer] Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a parallelogram. Statements - Brainly.com Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a parallelogram. Statements Reasons 1.

Which pair of sides of ABCD are parallel to each other?

Prove: AB=CD and BC=DA - Brainly.com Given: ABCD is a parellelogram. We have given a parallelogram ABCD. Opposite pair of sides are parallel to each other. i.e AD is parallel to BC and AB is parallel to CD.

What is the congruent property of triangle ABCD?

[Expert Answer] Given: ABCD is a parellelogram. Prove: AB=CD and BC=DA - Brainly.com Given: ABCD is a parellelogram. We have given a parallelogram ABCD. Opposite pair of sides are parallel to each other. i.e AD is parallel to BC and AB is parallel to CD. hence, ΔABC ≅ ΔCDA , By Angle-Side-Angle (ASA) congruent property of triangle.

How to find parallel lines in a parallelogram?

Divide both sides of 2 x + 2 y = 360 ° by 2. 4. A B ¯ ∥ D C ¯, A D ¯ ∥ B C ¯ 4. If a transversal intersects two lines such that each pair of interior angles on a same side of a transversal are supplementary then the lines are said to be parallel. 5. ABCD is a parallelogram

How do you prove ABCD is a parallelogram?

If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. If — BC — AD and — BC ≅ — AD , then ABCD is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

What theorem can you use to prove the figure is a parallelogram?

Theorem 46: If both pairs of opposite sides of a quadrilateral are equal, then it is a parallelogram.

Which theorem can be used to prove that the quadrilateral ABCD is a parallelogram?

Parallelogram Theorem #1 Converse: If each of the diagonals of a quadrilateral divide the quadrilateral into two congruent triangles, then the quadrilateral is a parallelogram. Parallelogram Theorem #2 Converse: If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

What makes ABCD a parallelogram?

A parallelogram is a special type of quadrilateral that has both the pair of opposite sides parallel and equal. The given figure shows a parallelogram ABCD which has AB II CD and AD II BC. Also, AD = BC and AB = CD.

What are the theorems of parallelogram?

Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. HSG-SRT.

Which conclusions are valid given ABCD is a parallelogram?

One pair of opposite sides is congruent and parallel, so ABCD is a parallelogram. One pair of opposite sides is congruent, so ABCD is a parallelogram.

Does SSS work for quadrilaterals?

The SSS triangle congruence theorem states that if all 3 sides of one triangle are in proportion to all 3 sides of another triangle then those triangles are similar. It is observed that Side-Side-Side congruence is not sufficient to prove that two quadrilaterals are congruent.

Which of the following statements ensures that a quadrilateral is a parallelogram?

A quadrilateral is a parallelogram if both pair of opposite angles are congruent.

Is a parallelogram ASA?

0:0820:50Proving Parallelograms With Two Column Proofs - Geometry - YouTubeYouTubeStart of suggested clipEnd of suggested clipNow the fourth way is to show that opposite angles are congruent so if you could show that angle bMoreNow the fourth way is to show that opposite angles are congruent so if you could show that angle b is congruent to angle d and angle a is congruent to angle c then it's a parallelogram.

Under what conditions must ABCD be a parallelogram?

If you have a quadrilateral that has diagonals that bisect each other, your quadrilateral is a parallelogram. Figure 16.4 shows a parallelogram ABCD with diagonals AC and BD that intersect at M and bisect each other.

How do you verify a parallelogram?

Well, we must show one of the six basic properties of parallelograms to be true!Both pairs of opposite sides are parallel.Both pairs of opposite sides are congruent.Both pairs of opposite angles are congruent.Diagonals bisect each other.One angle is supplementary to both consecutive angles (same-side interior)More items...•

How do you prove each of the following properties of a parallelogram?

Properties of parallelogramsOpposite sides are congruent (AB = DC).Opposite angels are congruent (D = B).Consecutive angles are supplementary (A + D = 180°).If one angle is right, then all angles are right.The diagonals of a parallelogram bisect each other.More items...

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