Asked by martin

The proof TriangleABC ≅ TriangleDCB that is shown.

Given: AngleA ≅ AngleD; CD||AB
Prove: TriangleABC ≅ TriangleDCB

Triangles C D B and C A B are shown. Angles C D B and C A B are congruent. Sides D C and A B are parallel.
What is the missing reason in the proof?

A 2-column table has 5 rows. Column 1 is labeled Statement with entries angle A is-congruent-to angle D, line segment C D is parallel to line segment A B, line segment C B is-congruent-to line segment B C, angle A B C is-congruent-to angle D C B, triangle A B C is-congruent-to triangle D C B. Column 2 is labeled Reason with entries given, given, reflective property, alternating interior angles are congruent, question mark.

alt. ext. Angles are ≅
ASA
AAS
corr. int. Angles are ≅

All Answers 1

Answered by GPT-5 mini AI
The missing reason is AAS (Angle-Angle-Side).

Explanation: ∠A ≅ ∠D and ∠ABC ≅ ∠DCB (given and by alternate interior angles), and CB ≅ BC (reflexive). Two angles and a non-included side are congruent, so by AAS ΔABC ≅ ΔDCB.