Question

Which rule explains why these triangles are congruent?

A. ASA
B. AAS
C. SAS
D. These triangles cannot be proven congruent.

Answer 1

D. These triangles cannot be proven congruent.

Explanation:

These triangles cannot be proven congruent.

Congruent angles are indicated on the diagram by the same number of arcs. Therefore:

• ∠U ≅ ∠W
• ∠V ≅ ∠X

According to the Vertical Angle Theorem, opposite vertical angles of two straight intersecting lines are congruent. Therefore:

• ∠WTX ≅ ∠UTV

Therefore, the corresponding angles of ΔUTV and ΔWTX are congruent.

As we don't know if the corresponding sides of the two triangles are congruent, we cannot prove that the triangles are congruent. Instead we can say that the two triangles are similar since their corresponding angles are the same size.