Question

for each pair of triangles, determine whether the hypotenuse - leg (hl) congruence property can be used to prove that the triangles are congruent. if necessary, you may learn what the markings on a figure indicate.

Explanation:

Step1: Recall the HL Congruence Property

The Hypotenuse - Leg (HL) Congruence Property 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.

Step2: Analyze each pair of triangles

• (a)
• These are right - triangles. The hypotenuse (\(30\) cm) and a leg (\(18\) cm) of one triangle are congruent to the hypotenuse (\(30\) cm) and a leg (\(18\) cm) of the other triangle. So, the HL property can be used.
• (b)
• These are right - triangles. But we are given the legs (marked as equal) and no information about the hypotenuses. The HL property requires the hypotenuse and a leg. So, the HL property cannot be used.
• (c)
• These are not right - triangles. The HL property is only for right - triangles. So, the HL property cannot be used.
• (d)
• These are right - triangles. The hypotenuse (the common side) and a leg (marked as equal) of one triangle are congruent to the hypotenuse (the common side) and a leg (marked as equal) of the other triangle. So, the HL property can be used.

Answer:

(a) Yes; (b) No; (c) No; (d) Yes