Question

D is the midpoint of AC, BA ≅BC and ∠EDA ≅ ∠FDC. Prove ΔAED ≅ ΔCFD

Answer 1

We are asked to prove that triangles AED and CFD are congruent. To do that we will prove that we can use the ASA (Angle Side Angle) rule of congruency.

First, we are given that D is a midpoint of segment AC, therefore:

`\bar{AD}=\bar{AC}`

Also, we are given that:

`\bar{BA}=\bar{BC}`

This means that triangle ABC is an isosceles triangle and therefore, its base angles are equal. This means that:

`\angle BAC=\angle BCA`

And, since we are given that angles EDA and FDC are equal, then by ASA we can conclude that:

`\Delta AED\cong\Delta CFD`