Question

Prove triangles ABC and DEF are similar.
Given:
AB BC AC
DE EF DF

Answer 1

Δ ABC ~ Δ DEF ......{By Converse of Side-Side-Side Similarity test}..Proof is given below.

Explanation:

Given:

`(AB)/(DE) =(BC)/(EF) =(AC)/(DF)`..........Given

To Prove

Δ ABC ~ Δ DEF

Proof:

In Δ ABC and Δ DEF

`(AB)/(DE) =(BC)/(EF) =(AC)/(DF)`..........Given

Which are the corresponding sides of similar triangles in proportion.

We know that If two triangles are similar then their corresponding sides are in proportion.

∴ Δ ABC ~ Δ DEF ......{By Converse of Side-Side-Side Similarity test}..Proved