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. (a) image of two right triangles with a 36 km leg each (b) image of two right triangles with marked sides (c) image of two triangles with marked angles and sides (d) image of two right triangles with marked sides can the hl congruence property be used? (a) yes / no (b) yes / no (c) yes / no (d) yes / no

Explanation:

Step1: Recall HL congruence rules

HL applies only to right triangles, requiring 1 pair of congruent hypotenuses and 1 pair of congruent corresponding legs.

Step2: Analyze pair (a)

Both are right triangles. They share a 36 km hypotenuse, but no congruent legs are marked.

Step3: Analyze pair (b)

Both are right triangles. They have 1 congruent leg (marked ticks) and 1 congruent hypotenuse (marked ticks).

Step4: Analyze pair (c)

These are not right triangles (no right angle markers), so HL does not apply.

Step5: Analyze pair (d)

Both are right triangles. They share a common hypotenuse, and 1 pair of congruent legs (marked ticks).

Answer:

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