Question

given: △dfh and △egi are equiangular. prove: ∠d≡∠egi

Explanation:

Step1: State the given

Given $\triangle DFH$ and $\triangle EGI$ are equiangular.

Step2: Identify corresponding angles

Since they are equiangular, corresponding angles are congruent and $\angle D$ and $\angle EGI$ are corresponding.

Step3: Conclusion

So, $\angle D\cong\angle EGI$.

Answer:

1. Given: $\triangle DFH$ and $\triangle EGI$ are equiangular.
2. Definition of equiangular triangles: Corresponding angles of equiangular triangles are congruent. $\angle D$ and $\angle EGI$ are corresponding angles.
3. $\angle D\cong\angle EGI$: By the property of corresponding - angles of equiangular triangles.