Question

(b) problem 12: (first taught in lesson 35)
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 right - triangle parts

We have two right - triangles $\triangle AKI$ and $\triangle CEG$. The hypotenuse and one leg of one right - triangle are equal to the hypotenuse and one leg of the other right - triangle. In right - triangle $\triangle AKI$, the hypotenuse is $AI$ and a leg is $KI$. In right - triangle $\triangle CEG$, the hypotenuse is $CG$ and a leg is $EG$. Given that $AI = CG$ (hypotenuses are equal) and $KI=EG$ (legs are equal).

Step2: Apply the theorem

The Hypotenuse - Leg (HL) Theorem 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, by the HL Theorem, $\triangle AKI\cong\triangle CEG$.

Answer:

Hypotenuse - Leg (HL) Theorem