Chapter 6, Problem 16CT

To determine

To calculate: the unknown side lengths and name the corresponding angles and side lengths in $\Delta \text{ABC}\cong \Delta \text{EFG}$ .

Answer to Problem 16CT

The corresponding angles are

  $\begin{array}{l}\angle \text{ABC}\cong \angle EFG\\ \angle \text{ACB}\cong \angle EGF\\ \angle BA\text{C}\cong \angle FEG\end{array}$

The corresponding side lengths are

  $\frac{AB}{EF}=\frac{BC}{FG}=\frac{AC}{EG}$

For unknown length substitute value in the corresponding side lengths

  $\begin{array}{l}EF=1m\\ BC=3m\\ AC=2.5m\end{array}$

Explanation of Solution

Given information : from figure provided in the question it is observed that,

  $\begin{array}{l}AB=1m\\ GF=3m\\ EG=2.5m\end{array}$

Calculation : the corresponding angles are

  $\begin{array}{l}\angle \text{ABC}\cong \angle EFG\\ \angle \text{ACB}\cong \angle EGF\\ \angle BA\text{C}\cong \angle FEG\end{array}$

The corresponding sides lengths are,

  $\frac{AB}{EF}=\frac{BC}{FG}=\frac{AC}{EG}$

For unknown length substitute value in the corresponding side lengths,

  $\begin{array}{l}\frac{AB}{EF}=\frac{BC}{FG}=\frac{AC}{EG}\\ \frac{1}{EF}=\frac{BC}{3}=\frac{AC}{2.5}\text{ [because of similliar triangles equal the sides]}\\ EF=1m\\ BC=3m\\ AC=2.5m\end{array}$

Hence,

The corresponding angles are

  $\begin{array}{l}\angle \text{ABC}\cong \angle EFG\\ \angle \text{ACB}\cong \angle EGF\\ \angle BA\text{C}\cong \angle FEG\end{array}$

The corresponding side lengths are

  $\frac{AB}{EF}=\frac{BC}{FG}=\frac{AC}{EG}$

For unknown length substitute value in the corresponding side lengths

  $\begin{array}{l}EF=1m\\ BC=3m\\ AC=2.5m\end{array}$