Prove theorems about parallelograms: opposite sides are congruent; opposite angles are congruent; diagonals of a parallelogram bisect each other and conversely rectangles are parallelograms with congruent diagonals.

Sample Practice Questions (3)

Given parallelogram

A B C D

with diagonal

\overline{A C}

, complete the proof to show that

△ A B C ≅ △ C D A

Statement	Reason
1. ABCD is a parallelogram	1. Given
2. AB \|\| CD, BC \|\| DA	2. ?
3. Angle BAC congruent to Angle DCA	3. ?
4. AC congruent to AC	4. ?
5. Triangle ABC congruent to Triangle CDA	5. ?

Open response · diagram · tableSee Answer + Explanation →

In parallelogram

E F G H

E F = 5 y

and

F G = 3 y + 2

. If the perimeter of the parallelogram is

68

units, what is the value of

y

4

8.25

5

2

In parallelogram

W X Y Z

, the measure of

∠ W

x

and the measure of

∠ X

3 x - 20

. Find

m ∠ W

in degrees.

5 0^{\circ}

13 0^{\circ}

4 0^{\circ}

1 0^{\circ}

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