Question

1. for two right triangles to be congruent, which of the following must be true? their corresponding angles must be proportional. their corresponding sides and angles must be equal in measure. only their corresponding sides must be equal in measure. their corresponding angles must be equal in measure and corresponding sides must be proportional.

Explanation:

1. Recall the definition of congruent triangles: Congruent triangles have all corresponding sides equal in length and all corresponding angles equal in measure.
2. Analyze each option:

• Option 1: Corresponding angles being proportional is a property of similar triangles, not congruent. So this is incorrect.
• Option 2: This matches the definition of congruent triangles (both corresponding sides and angles are equal).
• Option 3: Just corresponding sides being equal is not sufficient for congruence (e.g., SSA is not a congruence criterion for all triangles, and even for right triangles, we need more, but the definition of congruence requires both sides and angles to be equal). So this is incorrect.
• Option 4: Corresponding angles equal and sides proportional is the definition of similar triangles, not congruent. So this is incorrect.

Answer:

B. Their corresponding sides and angles must be equal in measure.