Chapter 4.5, Problem 21WE

To determine

Show $\overline{AE}\cong \overline{FC}\cong \overline{ND}$

Explanation of Solution

Given:

The diagram shows three squares and an equilateral triangle.

Calculation:

The diagram is :

  

Since triangle CDE is equilateral and the three squares have one side as a side of the equilateral triangle.

So, $\overline{AD}\cong \overline{DE}\cong \overline{FE}\cong \overline{EC}\cong \overline{NC}\cong \overline{CD}$

In the isosceles triangles ADE , FEC , and NCD :

  $\angle DAE\cong \angle DEA\cong \angle EFC\cong \angle ECF\cong \angle DNC\cong \angle CDN$ , since all the equal sides of the triangles are congruent , so all the base angles will also be congruent.

So, $\Delta ADE\cong \Delta FEC\cong \Delta NCD$

So, $\overline{AE}\cong \overline{FC}\cong \overline{ND}$

Hence proved.