Prove that triangle $\triangle ABC \cong \triangle G H I$ . Explain each step.

Question

My question:

Prove that triangle $\triangle ABC \cong \triangle G H I$ . Explain each step.

Here are my triangles

I proved that $\triangle ABC \cong\triangle DEF$ because the first sign of equality.

1. angle $ABC = $angle $DEF$
2. $AB = DE$
3. $BC = EF$

Now my problem is how to prove $\triangle ABC \cong \triangle G H I$.

Thanks again!

Answer 1

First you should prove that $\triangle DEF \cong \triangle GHI$ by applying the ASA (Angle-Side-Angle) criterion:

angle $EDF \cong$ angle $HGI$;

$DF \cong GI$;

angle $DFE \cong$ angle $GIH$.

Finally you can prove that $\triangle ABC \cong \triangle GHI$ by applying the transitive property of congruence.