Question

Assume that AABC= APQR. Which of the following congruence statements are correct? Check all that apply.

A. BC = PQ
B. ∠CE ≅ ∠P
C. AB = PO
D. ∠RE ≅ ∠C
E. ∠A = 20
F. AC = QR

Answer 1

In the congruence statement ΔABC ≅ ΔPQR, BC = PQ and AC = QR are correct because corresponding sides in congruent triangles are equal. Other provided options either do not refer to corresponding parts or do not provide enough information to verify congruence.

Step-by-step explanation:

Assuming that triangle ABC is congruent to triangle PQR, we can determine the correct congruence statements based on the facts provided in the question. When two triangles are congruent, it means that their corresponding sides and angles are equal in measure. Given the congruence statement ΔABC ≅ ΔPQR, we can make the following conclusions:

• BC = PQ - This is correct because corresponding sides in congruent triangles are equal.
• ∠CE ≃ ∠P - This cannot be determined as ∠CE and ∠P are not specified as corresponding angles in the given congruence statement, or even part of the triangles.
• AB = PO - This is incorrect because PO is not a side of triangle PQR, and AB corresponds to PQ or PR, not PO.
• ∠RE ≃ ∠C - We cannot confirm this as angle RE is not clearly defined as part of triangle PQR or its relation to ∠C.
• ∠A = 20 - This could be correct if ∠A indeed measures 20 degrees, but this is a value statement, not a congruence statement.
• AC = QR - This is correct because corresponding sides in congruent triangles are equal.