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

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

Step-by-step 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 :-

$\frac{DF}{GF}=\frac{FE}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{DG+GF}{GF}=\frac{FH+EH}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{5+15}{5}=\frac{12+HF}{FH}=\frac{8}{GH}\\\\\Rightarrow\frac{20}{5}=\frac{12+HF}{FH}\ and\ \frac{20}{5}=\frac{8}{GH}\\\\\Rightarrrow4HF=12+HF\ and\ GH=\frac{8}{4}\\\\\Rightarrow3HF=12\ and\ GH=2\\\\\Rightarrow HF=4\ and\ GH=2$

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.

Answer 2

Answer:

C

Step-by-step explanation: