Chapter 8.5, Problem 17PSB

To determine

To show that three ratios are equal.

Explanation of Solution

Given information:

WYZB is Trapezoid with bases $\overline{WB}$ and $\overline{YZ}$ .

  $\overleftrightarrow{XA}$ is parallel to $\overline{YZ}$ .

Formula used:

The below property is used:

If three or more parallel lines intersect two transversals, they divide them.

Proof:

  

It is given that, WYZB is Trapezoid with bases $\overline{WB}$ and $\overline{YZ}$ .

  $\overleftrightarrow{XA}$ is parallel to $\overline{YZ}$ .

Bases of Trapezoidal are parallel.

  $\overleftrightarrow{WB}$ is parallel to $\overline{YZ}$ .

According to Transitive property of parallel lines, we get

  $\overleftrightarrow{XA}$ is parallel to $\overleftrightarrow{WB}$ and $\overline{YZ}$ .

If three or more parallel lines intersect two transversals, they divide them.

  $\frac{WX}{XY}=\frac{BA}{AZ}$ ---- Equation 1

  $\frac{WX}{XY}=\frac{WC}{CZ}$ ---- Equation 2

From Equation 1 and Equation 2, we get

  $\frac{WX}{XY}=\frac{BA}{AZ}=\frac{WC}{CZ}$