Question

7 which statement belongs in the two - column proof for the right triangles in place of letter d? statements reasons a ab ≅ rs given b ∠c and ∠t are right angles given c △abc and △rst are right triangles definition of right triangles d △abc ≅ △rst hl theorem

Explanation:

Step1: Identify right - angled triangles

We see that $\angle C = 90^{\circ}$ and $\angle T=90^{\circ}$, so $\triangle ABC$ and $\triangle RST$ are right - angled triangles. This is based on the definition of right - angled triangles (a triangle with one angle equal to 90 degrees).

Step2: Check hypotenuse - leg (HL) congruence

We are given that $AB\cong RS$ (hypotenuses) and from the markings on the sides, we assume the legs are also congruent. By the HL (Hypotenuse - Leg) theorem, which states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.

Answer:

$\triangle ABC\cong\triangle RST$ (by HL theorem)