Question

Assume that triangle ABC is congruent to triangle PQR. Which of the following congruence statements is/are correct? Check all that apply.

A. AB ≅ PQ

B. BC ≅ PQ

C. ∠C ≅ ∠P

D. AC ≅ QR

E. ∠A ≅ ∠Q

F. ∠R ≅ ∠C

Answer 1

Triangle ABC is congruent to triangle PQR, meaning all corresponding sides and angles are congruent. Statements AB ≅ PQ, BC ≅ QR, ∠C ≅ ∠R, AC ≅ PR, and ∠A ≅ ∠Q are correct. The congruence assures that each part of one triangle has a matching part in the other triangle with the same measurement.

Step-by-step explanation:

When triangles are congruent, all corresponding sides and angles are equal in measure. In this case, since triangle ABC is congruent to triangle PQR, we can determine which congruence statements are correct.

• AB ≅ PQ: This statement is correct. Since the triangles are congruent, side AB in triangle ABC corresponds to side PQ in triangle PQR.
• BC ≅ QR: This statement is also correct for the same reasoning.
• ∠C ≅ ∠R: Given the congruency, the angles at points C and R must also be congruent.
• AC ≅ PR: This is correct since AC in triangle ABC corresponds to PR in triangle PQR due to congruency.
• ∠A ≅ ∠Q: As with the sides, the angles at points A and Q are congruent.
• ∠B ≅ ∠P: While not listed in the options, it's important to note that this angle pair is also congruent.

Note that congruence is a precise term meaning all corresponding sides and angles match. If triangle ABC is congruent to triangle PQR, the congruence statement would usually be written as △ABC ≅ △PQR, indicating that vertex A corresponds to P, B to Q, and C to R. The triangles not only have the same shapes and sizes, but their corresponding angles and sides are equal.