Chapter 4.2, Problem 25WE

To determine

To draw: and label a diagram, and to proved the given statement.

Explanation of Solution

Given information:

Given statement,

Pentagon $ABCDE$ is equilateral and has right angles at $B$ and $E$ , then diagonals $\overline{AC}$ and $\overline{AD}$ form congruent triangles.

Calculation:

SSS Postulate: If three sides of a triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

SAS Postulate: If two sides and the angle included between them of a triangle are equal to the two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.

ASA Postulate: If two angles and the included side of a triangle are equal to the two corresponding angles and the included side of another triangle, then the triangles are congruent.

  

Given $ABCDE$ is an equilateral pentagon;

  $\angle B=\angle E=90°$

Prove: $\Delta ABC\cong \Delta AED$

Proof:

  $AB=DE$ & $BC=AE$

Reason: $ABCDE$ is an equilateral pentagon

  $\angle B=\angle E=90°$

Reason: Given

  $\Delta ABC\cong \Delta AED$

Reason: $SAS$ postulate.