Question

given: ad ≅ bc and ad ∥ bc
prove: abcd is a parallelogram.
statements

1. ad ≅ bc; ad ∥ bc
2. ∠cad and ∠acb are alternate interior ∠s
3. ∠cad ≅ ∠acb
4. ac ≅ ac
5. △cad ≅ △acb
6. ab ≅ cd

reasons

1. given
2. definition of alternate interior angles
3. alternate interior angles are congruent
4. reflexive property
5. sas congruency theorem

6.?

Explanation:

Step1: Recall congruent - triangle properties

Since $\triangle CAD\cong\triangle ACB$ (by SAS congruency theorem), corresponding parts of congruent triangles are congruent.

Step2: Identify corresponding sides

In congruent triangles $\triangle CAD$ and $\triangle ACB$, $\overline{AB}$ and $\overline{CD}$ are corresponding sides.

Answer:

Corresponding parts of congruent triangles are congruent.