Parallelograms — Quiz

Question 23 • Math 3

Which sequence could be used to prove that AD is equal to BC ?

Answer

First prove triangle ABC is similar to triangle CDA , and then state line segment AD and line segment BC are opposite sides of the parallelograms.

First prove triangle ABC is congruent to triangle CDA , and then state line segment AD and line segment BC are corresponding sides of the triangles.

First prove parallelogram ABCD is congruent to parallelogram CDAB , and then state line segment AD and line segment BC are corresponding sides of two parallelograms.

First prove parallelogram ABCD is similar to parallelogram CDAB , and then state line segment AD and line segment BC are opposite sides of the parallelograms.

Explanation

If triangles ABC and CDA are congruent, their corresponding sides have equal lengths. In that correspondence, side BC matches side AD, so AD = BC. Choice D gives a valid sequence; the other choices either use similarity, which does not establish equal side lengths, or rely on opposite sides of a parallelogram without first establishing that ABCD is a parallelogram.

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