Chapter 13, Problem 5CUR

a.

To determine

To show: that $\angle B\cong \angle D$ .

Explanation of Solution

Given information: The figure shown below:

  

Proof:

  $\begin{array}{l}\angle AEB=\angle DEC\\ \frac{AE}{EC}=\frac{8}{12}=\frac{2}{3}\\ \frac{BE}{ED}=\frac{6}{9}=\frac{2}{3}\\ \Delta AEB\&\Delta CED\text{ are similiar}\\ \angle AEB=\angle CDE\\ \angle B\cong \angle D\end{array}$

b.

To determine

To find: the value of $x$ .

Answer to Problem 5CUR

The value of $x$ is $18$ .

Explanation of Solution

Given information: The figure shown below:

  

Calculation:

  $\begin{array}{l}\frac{AE}{EC}=\frac{AB}{CD}\\ \frac{8}{12}=\frac{12}{x}\\ x=12\times \frac{3}{2}\\ x=18\end{array}$

c.

To determine

To find: the ratio of areas of triangle.

Answer to Problem 5CUR

The ratio of areas of triangle is $\frac{4}{9}$ .

Explanation of Solution

Given information: The figure shown below:

  

Calculation:

  $\begin{array}{l}\frac{ar\left(\Delta ABE\right)}{ar\left(\Delta CED\right)}\\ \Rightarrow \frac{8}{12}=\frac{2}{3}\\ \frac{ar\left(\Delta ABE\right)}{ar\left(\Delta CED\right)}={\left(\frac{2}{3}\right)}^2=\frac{4}{9}\end{array}$