Question

are the two triangles congruent? if so, write the congruence statement. choose the correct answer below. o a. yes, △def ≅ △jhg by the hl theorem. o b. yes, △def ≅ △jgh by the hl theorem. o c. yes, △def ≅ △ghj by the hl theorem. o d. yes, △def ≅ △gjh by the hl theorem. o e. no, the triangles are not congruent.

Explanation:

Step1: Use 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.
In \(\triangle DEF\) and \(\triangle GHJ\), \(DF = GJ = 5\) (hypotenuses) and \(EF=HJ = 3\) (legs).

Step2: Check the congruence statement order

The order of the vertices in the congruence statement should match the corresponding vertices. In \(\triangle DEF\) and \(\triangle GHJ\), \(D\) corresponds to \(G\), \(E\) corresponds to \(H\), and \(F\) corresponds to \(J\). So the congruence statement is \(\triangle DEF\cong\triangle GHJ\) by the HL theorem.

Answer:

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