Question

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

A) HF is 2 units and GH is 3 units.
B) HF is 3 units and GH is 2 units.
C) HF is 4 units and GH is 2 units.
D) HF is 3 units and GH is 4 units.

Answer 1

C

Explanation:

Answer 2

Answer: C) HF is 4 units and GH is 2 units.

Explanation:

The SSS similarity theorem says that if the side-lengths of the corresponding sides of two triangles are proportional then the triangles are similar.

In ΔDFE and ΔGFH ,

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

To prove ΔDFE and ΔGFH are similar by using SSS similarity theorem we need :-

`(DF)/(GF)=(FE)/(FH)=(DE)/(GH)\\\\\Rightarrow(DG+GF)/(GF)=(FH+EH)/(FH)=(DE)/(GH)\\\\\Rightarrow(5+15)/(5)=(12+HF)/(FH)=(8)/(GH)\\\\\Rightarrow(20)/(5)=(12+HF)/(FH)\ and\ (20)/(5)=(8)/(GH)\\\\\Rightarrrow4HF=12+HF\ and\ GH=(8)/(4)\\\\\Rightarrow3HF=12\ and\ GH=2\\\\\Rightarrow HF=4\ and\ GH=2`

Hence, 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 4 units and GH is 2 units.