Question

ABC is an isosceles triangle, which means that line segment AB and AC are congruent. APQ is isosceles which means line segments BP and QC are

congruent. Which of the triangles in the following figure are congruent?
Α:ΑΒΡ and AQC
Β:ABC and APQ
C:ΑΒΡ and APC
D:APQ and AQC

Answer 1

In the given figure, the congruent triangles are ABΡ and AQC, and ABC and APQ.

Step-by-step explanation:

In the given figure, the congruent triangles are:

1. ABΡ and AQC
2. ABC and APQ

To determine the congruent triangles, we observe that triangles with equal side lengths and equal angles are congruent. In triangle ABC, AB and AC are congruent due to the isosceles triangle property. In triangle APQ, BP and QC are congruent due to the isosceles triangle property. Therefore, triangles ABΡ and AQC are congruent as they have equal side lengths and equal angles. Similarly, triangles ABC and APQ are congruent as they have equal side lengths and equal angles.