Question

2.△abc and △pqr are right triangular sections of a fire escape, as shown. is each story of the building the same height? explain.
choose the correct answer below.
a. no, because the hypotenuse ac is not congruent to the hypotenuse pr.
b. no, because the leg ab is not congruent to the leg pq.
c. yes, because the triangles are congruent by the hypotenuse - leg theorem. so, bc ≅ qr.
d. yes, because the triangles are congruent by the third angles theorem. so, ∠c ≅ ∠r.

Explanation:

Step1: Check Hypotenuse - Leg Congruence

In right - angled triangles, the Hypotenuse - Leg (HL) Theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two triangles are congruent.
From the image, we can assume that the hypotenuses \(AC\) and \(PR\) are congruent (since they are part of the same - structured fire - escape sections) and the legs \(BC\) and \(QR\) are congruent (by visual inspection of the similar - looking steps).
So, \(\triangle ABC\cong\triangle PQR\) by the Hypotenuse - Leg Theorem.

Answer:

C. Yes, because the triangles are congruent by the Hypotenuse - Leg Theorem