Question

can the hl congruence property be used? (a) 16 km 16 km 34 km 34 km (b) (c) (d)

Explanation:

Step1: Recall HL Congruence Property

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 each triangle is \(34\) km and a leg of each triangle is \(16\) km. Since both are right - triangles (they have a right - angle) and the hypotenuse and a leg are equal, HL can be used.

Step3: Analyze Part (b)

In part (b), we have two right - triangles. But we do not know the lengths of the hypotenuse and the leg. Just having a mark (which may represent congruent sides) is not sufficient as we don't know if it is the hypotenuse and a leg. So, HL cannot be used.

Step4: Analyze Part (c)

In part (c), the triangles are not right - triangles. HL Congruence Property is only for right - triangles. So, HL cannot be used.

Step5: Analyze Part (d)

In part (d), we have two right - triangles (formed by the diagonal of the rectangle). The hypotenuse (the diagonal) is common (so congruent) and one leg (the side of the rectangle which is marked as congruent). So, HL can be used.

Answer:

a. Yes
b. No
c. No
d. Yes