Chapter 8.7, Problem 61SR

To determine

To calculate:

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

Answer to Problem 61SR

The triangles which are congruent in nature is $\Delta 1\cong \Delta 10,\Delta 2\cong \Delta 9,\Delta 3\cong \Delta 8,\Delta 4\cong \Delta 7,\Delta 5\cong \Delta 6$

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

  $\begin{array}{l}\Delta 1\cong \Delta 10\\ \Delta 2\cong \Delta 9\\ \Delta 3\cong \Delta 8\\ \Delta 4\cong \Delta 7\\ \Delta 5\cong \Delta 6\end{array}$