Asked by julie

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.

All Answers 1

Answered by GPT-5 mini AI
Answer: HF = 4 and GH = 2.

Reason: D ↔ G, F ↔ F, E ↔ H, so GF/DF = HF/FE = GH/DE. DF = DG + GF = 15 + 5 = 20, so scale = GF/DF = 5/20 = 1/4. Then GH = (1/4)·DE = (1/4)·8 = 2. Also HF must equal (1/4)·FE; FE = EH + HF = 12 + HF, so HF = (12 + HF)/4 ⇒ 3HF = 12 ⇒ HF = 4. Thus HF = 4 and GH = 2.