Question

Tell weather DEF and GEF can be proven congruent.

A) Yes, DEF and GEF can be proven congruent by SSS.
B) No, DEF and GEF aren’t congruent because they share a side.
C) No, there isn’t enough information provided.
D) Yes, DEF and GEF can be proven congruent by HL.

Answer 1

D) Yes, DEF and GEF can be proven congruent by HL.

Explanation:

Given triangles DEF and GEF with sides DF and GF marked congruent, and a right angle at E, you want to know if congruence can be proved, and how.

Congruence

The hypotenuses of the right triangles are marked congruent. The shared leg EF is congruent to itself, so enough information is provided to claim congruence by the HL theorem.

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Additional comment

Sides DE and GE are not marked congruent, so you only can make claims about 2 of the sides. SSS congruence cannot apply.

The HL theorem only applies to right triangles, which these are.