Chapter 11, Problem 16CUR

To determine

To Find:

Method to be used to prove that diagonal of an equilateral quadrilateral forms two congruent triangles.

Answer to Problem 16CUR

  $S-A-S$ congruence.

Explanation of Solution

Given:

An equilateral quadrilateral with its diagonal drawn.

An equilateral quadrilateral is one which has all of its four sides equal to each other.

Examples are:

1. Square
2. Rhombus

Kindly refer to the diagram:

  

$ABCD$ is the equilateral quadrilateral with its diagonal $BD$ dividing it in two triangles $\Delta ADB,\Delta CBD$ .

  $AD\cong BC$

  $\angle A\cong \angle C$

  $AB\cong CD$

  $S-A-S$ congruence: $\Delta ADB\cong \Delta CBD$