Question

which of the following describes the relationship between the given triangles? △pnm≅△acb by the ssa congruence theorem △pnm≅△acb by the hl congruence theorem △pnm≅△cab by the hl congruence theorem none of these

Explanation:

Step1: Identify right - angled triangles

Both $\triangle PNM$ and $\triangle ACB$ have right angles at $\angle N$ and $\angle C$ respectively.

Step2: Check congruent sides

The hypotenuse and one leg of $\triangle PNM$ are congruent to the hypotenuse and one leg of $\triangle ACB$ (shown by the tick marks).

Step3: Apply HL theorem

The HL (Hypotenuse - Leg) congruence 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, the two right - triangles are congruent. So, $\triangle PNM\cong\triangle ACB$ by the HL congruence theorem.

Answer:

B. $\triangle PNM\cong\triangle ACB$ by the HL congruence theorem