Chapter 8.7, Problem 62SR

To determine

To calculate:

The triangles which are congruent in nature by using the following figure:

Answer to Problem 62SR

The triangles which are congruent in nature is

  $\begin{array}{l}\Delta 1\cong \Delta 2\cong \Delta 3\cong \Delta 4:\\ \Delta 5\cong \Delta 6\cong \Delta 7\cong \Delta 8\cong \Delta 9\cong \Delta 10\cong \Delta 11\cong \Delta 12:\\ \Delta 13\cong \Delta 14\cong \Delta 15\cong \Delta 16\cong \Delta 17\cong \Delta 18\cong \Delta 19\cong \Delta 20.\end{array}$

Explanation of Solution

Given information:

  

Calculation:

Here, need to assume the segments and angles of the following figure as congruent to determine which triangle are congruent in nature:

  

From observation of the figure:

Use the symmetry of bridge to the congruent corresponding the sides between the triangles.

It has

  $\begin{array}{l}\Delta 1\cong \Delta 2\cong \Delta 3\cong \Delta 4:\\ \Delta 5\cong \Delta 6\cong \Delta 7\cong \Delta 8\cong \Delta 9\cong \Delta 10\cong \Delta 11\cong \Delta 12:\\ \Delta 13\cong \Delta 14\cong \Delta 15\cong \Delta 16\cong \Delta 17\cong \Delta 18\cong \Delta 19\cong \Delta 20.\end{array}$