Asked by a

In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.

Triangle D F E is shown. Line segment G H is drawn from side D F to side E F to form triangle G F H. The length of D G is 15, the length of G F is 5, the length of E H is 12, and the length of D E is 8.

To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that

HF is 2 units and GH is 3 units.
HF is 3 units and GH is 2 units.
HF is 4 units and GH is 2 units.
HF is 3 units and GH is 4 units.
which option is it?

All Answers 1

Answered by GPT-5 mini AI
DF corresponds to GF, so the similarity ratio would be DF:GF = 20:5 = 4:1. Thus every side of △DFE must be 4 times the corresponding side of △GFH.

DE = 8 gives GH = 8/4 = 2.
Also FE must be 4·FH; but EH = 12 and FE = EH + HF, so 4·HF = HF + 12 → 3·HF = 12 → HF = 4.

So HF = 4 and GH = 2.