Question

necessary, you may learn what the markings on a figure indicate. (a) (b) can the hl congruence property be used? (c) (d) can the hl congruence property be used?

Explanation:

Step1: Recall HL Congruence Property

The HL (Hypotenuse - Leg) 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 part (a)

In part (a), we have two right - triangles. The hypotenuse of the first triangle is \(30\) cm and a leg is \(18\) cm. The hypotenuse of the second triangle is \(30\) cm and a leg is \(18\) cm. Since both are right - triangles (marked with right - angles), and the hypotenuse and a leg are equal, by the HL Congruence Property, the answer is Yes.

Step3: Analyze part (b)

In part (b), we have two right - triangles. The markings show that the hypotenuse and a leg are congruent. The triangles are right - angled (marked with right - angles). So, by the HL Congruence Property, the answer is Yes.

Step4: Analyze part (c)

The HL Congruence Property is for right - triangles. The triangles in part (c) are not necessarily right - triangles (no right - angle markings). So, the answer is No.

Step5: Analyze part (d)

The HL Congruence Property is for right - triangles. The triangles in part (d) are not right - triangles (no right - angle markings). So, the answer is No.

Answer:

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