Question

triangles determining when to apply the hl congruence for each pair of triangles, determine whether the hypotenuse - leg (hl) congruence property can be used to congruent. if necessary, you may learn what the markings on a figure indicate. (a) (b) can the hl congruence property be used? yes no yes no (c) (d) can the hl congruence property be used? yes no yes no

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. So, we need to check if the triangles are right - angled and if we have information about hypotenuse and a leg.

Step2: Analyze part (a)

The triangles in part (a) are not right - angled. Since the HL Congruence Property is only for right - angled triangles, the answer is No.

Step3: Analyze part (b)

The triangles in part (b) are right - angled. We can assume (from the markings) that the hypotenuse and a leg are congruent. So, the answer is Yes.

Step4: Analyze part (c)

In part (c), we only know the length of one leg (\(4m\)) for each right - angled triangle. We have no information about the hypotenuse. So, the answer is No.

Step5: Analyze part (d)

In part (d), for the right - angled triangles, the markings show that the hypotenuse and a leg are congruent. So, the answer is Yes.

Answer:

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