Question

Hey, I'm dumb and need help.

Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. (10 points)

(The blanks below need to be filled in)

Let ABCD be a parallelogram. By definition of a ________, side AB is parallel to side CD and side BC is parallel to side DA. Construct diagonal BD using a straightedge. ∡ABD is congruent to ∡BDC by the _____ _____ ______ Theorem. By the same theorem, ∡CBD is congruent to ∡ADB. Segment BD is congruent to itself by the _____ Property of Equality. Therefore, ABD is congruent to CDB by _____ and opposite sides of parallelogram ABCD are congruent by _____.

Thank ye kindly.

Answer 1

Parallelogram.

Alternate Interior angle.

Reflexive.

ASA

Explanation:

AS for the last part i've only seen it in the States. Its something like CBCDC.

Basically it means the sides are congruent because they are corresponding sides of 2 congruent triangles.