Question

(b) problem 12: from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: △aki and △ceg are right triangles, ai = cg, and ki = eg prove: △aki ≅ △ceg

Explanation:

Step1: Identify triangle type

Given $\triangle AKI$ and $\triangle CEG$ are right - triangles.

Step2: Identify equal sides

We have $AI = CG$ (hypotenuses) and $KI=EG$ (legs).

Step3: Apply theorem

By the Hypotenuse - Leg (HL) 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. So, $\triangle AKI\cong\triangle CEG$.

Answer:

Hypotenuse - Leg (HL) Theorem