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) two right triangles with hypotenuse 25 m, leg 15 m (b) two triangles with marked sides (c) two right triangles with marked legs (d) a rectangle with a diagonal, forming 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 Congruence applies only to right triangles, requiring: 1) Both are right triangles; 2) Their hypotenuses are congruent; 3) One pair of corresponding legs are congruent.

Step2: Analyze Pair (a)

Both are right triangles. Hypotenuses ($25$ m) are congruent, and one pair of legs ($15$ m) are congruent.
Condition satisfied: HL applies.

Step3: Analyze Pair (b)

Triangles are not right triangles. HL only works for right triangles.
Condition not satisfied: HL does not apply.

Step4: Analyze Pair (c)

Both are right triangles, but the marked congruent sides are not corresponding: one triangle's leg matches the other's hypotenuse.
Condition not satisfied: HL does not apply.

Step5: Analyze Pair (d)

The two triangles formed are right triangles. They share a common hypotenuse, and one pair of corresponding legs (marked sides) are congruent.
Condition satisfied: HL applies.

Answer:

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