Theorem 9

Question 1

Theorem

Answer 1

In a parallelogram, opposite sides are equal and opposite angles are equal

Question 2

Given

Answer 2

A parallelogram ABCD

Question 3

Required to prove

Answer 3

|AB| = |DC| and |AD| = |BC|

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Question 4

Construction

Answer 4

Draw the diagonal [BD] and mark in angles 123 and 4

Question 5

Proof

Answer 5

In the triangles ABC and BCD
|<1| = |<3| … alternate angles and AB||DC
|<2| = |<4| … alternate angles
|DB| = |DB| … common side
.: 🔼’s ABD and BCD are congruent …ASA
.: |AB| = |DC| and |AD| = |BC| … corresponding sides
Also, |