Question

are the two triangles congruent? if so, write the congruence statement.
choose the correct answer below.
a. yes, △ghj≅△mkl by the hl theorem.
b. yes, △ghj≅△klm by the hl theorem.
c. yes, △ghj≅△mlk by the hl theorem.
d. yes, △ghj≅△kml by the hl theorem.
e. no, the triangles are not congruent.

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) theorem

The HL theorem 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: Identify the hypotenuse and leg in each triangle

In \(\triangle GHJ\), the hypotenuse \(GJ = 10\) and the leg \(JH=6\). In \(\triangle MLK\), the hypotenuse \(MK = 10\) and the leg \(ML = 6\).

Step3: Match the vertices for the congruence statement

For congruent triangles, we need to match the vertices. The right angle in \(\triangle GHJ\) is at \(H\), and the right angle in \(\triangle MLK\) is at \(L\). So, \(\triangle GHJ\cong\triangle MLK\) by the HL theorem.

Answer:

C. Yes, \(\triangle GHJ\cong\triangle MLK\) by the HL theorem.