Chapter 6.3, Problem 10PSC

To determine

Prove that $\mathrm{\Delta }\mathrm{A}\mathrm{D}\mathrm{E}$ is isosceles.

Answer to Problem 10PSC

  $\mathrm{\Delta }\mathrm{A}\mathrm{D}\mathrm{E}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{s}.$

Explanation of Solution

Given information:

Given: $\mathrm{m}\left|\right|\mathrm{n}$ , $\overline{\mathrm{B}\mathrm{D}}\cong \overline{\mathrm{C}\mathrm{E}}$

  

Calculation

Consider the given figure,

  

It is given that,

  $\mathrm{m}\left|\right|\mathrm{n}$ , $\overline{\mathrm{B}\mathrm{D}}\cong \overline{\mathrm{C}\mathrm{E}}$

If a plane intersects two lines the lines are parallel.

  $\overline{\mathrm{B}\mathrm{C}}\left|\right|\overline{\mathrm{D}\mathrm{E}}$

  $\mathrm{B}\mathrm{C}\mathrm{E}\mathrm{D}$ is an isosceles trapezoid,

  $\angle \mathrm{D}\cong \angle \mathrm{E}$ the base angles of an isosceles trapezoid are congruent,

The triangle with two congruent angles are isosceles,

Hence, $\mathrm{\Delta }\mathrm{A}\mathrm{D}\mathrm{E}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{s}.$