Given: ABCD is a quadrilateral, Segment AB is congruent to Segment CD, <1 is congruent to <2 Prove: ABCD is a parallelogra

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2 years ago

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tiny-mole [99] · Answer 1 · 2023-11-07T21:17:11+03:00

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.

We need to prove that ABCD is a parallelogram.

<h3>How to prove a given quadrilateral is a parallelogram?</h3>

If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.

From the given quadrilateral ABCD:

AB=CD (Given)

∠1=∠2 (Given)

AC=AC (Diagonal)

From ASA congruency ΔABC and ΔADC are congruent.

By CPCT, AD=BC and ∠ABC=∠ADC.

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

To learn more about parallelogram visit:

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