Question

HELP I WILL GIVE BRAINLIEST

Prove that in parallelogram both pairs of opposite angles are congruent (Theorem). Please provide an answer in the "statement and reason" format.

Answer 1

Explanation:

Statements are numbered; reasons are in italics.

1. ABCD is a parallelogram with AB≅CD and BC≅AD. Given; definition of a parallelogram.

2. Diagonal AC ≅ diagonal CA. Reflexive property of congruence.

3. ΔABC ≅ ΔCDA. SSS congruence postulate.

4. ∠B ≅ ∠D. CPCTC. (Opposite angles B and D are congruent.)

5. Diagonal BD ≅ diagonal DB. Reflexive property of congruence.

6. ΔABD ≅ ΔCDB. SSS congruence postulate.

7. ∠A ≅ ∠C. CPCTC. (Opposite angles A and C are congruent.)