Question

which theorem can you use to prove that △ ghj and △ gkj are congruent?

a. asa
b. sas
c. sss
d. hl

Explanation:

Step1: Identify triangle properties

Both \(\triangle GHJ\) and \(\triangle GKJ\) are right triangles (since \(\angle H\) and \(\angle K\) are right angles). \(GH = GK = 8\) (given), and \(GJ\) is a common hypotenuse for both triangles.

Step2: Recall congruence theorems

The Hypotenuse - Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. Here, hypotenuse \(GJ\) is common (so \(GJ\cong GJ\)), leg \(GH\cong GK\) (both 8), and both are right triangles. So HL theorem applies.

Answer:

D. HL