Question

Quadrilateral ABCD is a parallelogram. Segment BD is a diagonal of the parallelogram.

Which statement and reason correctly complete this proof?

Answer 1

(A) alternate interior angles

Explanation:

You want the missing statement in the proof that opposite angles of a parallelogram are congruent.

Proof

The proof here shows angles A and C are congruent because they are corresponding parts of congruent triangles. To get there, the triangles must be shown to be congruent.

In statement 5, the triangles area claimed congruent by the ASA theorem, which requires two corresponding pairs of angles and congruent sides.

In statement 4, the relevant sides are shown congruent, so it is left to statement 3 to show two pairs of angles are congruent.

Of the offered answer choices, only one of them deals with two pairs of angles. Answer choice A is the correct one.