Question

determine if the two triangles are congruent. if they are, state the postulate or theorem that proves they are congruent.

c d n

e p m

a. sss

b. hl

Explanation:

Step1: Identify Right Angles

Both triangles \( \triangle CDE \) and \( \triangle NPM \) have right angles (\( \angle D \) and \( \angle P \) are right angles), so they are right - angled triangles.

Step2: Identify Angle - Angle - Side (AAS) or Check HL

Looking at the angles: \( \angle C=\angle M \) (marked with the same number of arcs) and \( \angle E=\angle N \) (marked with the same number of arcs). Also, for right - angled triangles, the Hypotenuse - Leg (HL) theorem states that if the hypotenuse and one leg of a right - angled triangle are congruent to the hypotenuse and one leg of another right - angled triangle, then the triangles are congruent. In these two right - angled triangles, we can assume that the hypotenuse (e.g., \( CE \) and \( NM \)) and one leg (e.g., \( DE \) and \( PN \)) are congruent based on the angle markings (which imply some congruent relationships). The SSS (Side - Side - Side) postulate requires all three sides to be congruent, but we don't have information about all three sides. The HL theorem is applicable here as we are dealing with right - angled triangles and can establish hypotenuse - leg congruence.

Answer:

b. HL