Question

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

Explanation:

Step1: Identify right - angled triangles

We see that $\triangle ABC$ and $\triangle RST$ are right - angled triangles as $\angle C$ and $\angle T$ are right angles. This is based on the definition of right - angled triangles (a triangle with one angle equal to 90 degrees).

Step2: Check given side equalities

We are given that $CB\cong TS$ and $AB\cong RS$.

Step3: Apply HL theorem

In right - angled triangles, if the hypotenuse and one leg of one right - angled triangle are congruent to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent. Here, $AB$ and $RS$ are hypotenuses and $CB$ and $TS$ are legs. So, $\triangle ABC\cong\triangle RST$ by the HL (Hypotenuse - Leg) theorem.

Answer:

$\triangle ABC\cong\triangle RST$