Chapter 8.4, Problem 6PSA

To determine

To show that two sides are parallel to each other.

Answer to Problem 6PSA

  $ProductofWSandXYisequaltoproductofXSandWZ.$

Explanation of Solution

Given information:

  $\overleftrightarrow{\text{WZ}}\text{ is parallel to }\overleftrightarrow{\text{XY}}$

Formula used:

The below properties are used:

If a lines are parallel, then there corresponding angles are congruent.

Corresponding sides of similar triangles are proportional.

Means extremes product theorem:

If a product of a pair of not zero numbers is equal to the product of another pair of not zero numbers, then either pair of numbers be made the extremes, and the other pair the means, of proportion.

Proof:

  

It is given that,

  $\overleftrightarrow{\text{WZ}}\text{ is parallel to }\overleftrightarrow{\text{XY}}$

If a lines are parallel, then there corresponding angles are congruent.

  $\begin{array}{l}\angle \text{SWZ}\cong \angle \text{SXY}\\ \angle \text{SZW}\cong \angle \text{SYX}\end{array}$

By AA similarity rule, we get

  $\Delta \text{SZW}~ \Delta \text{SYX}$

Corresponding sides of similar triangles are proportional.

  $WS/XS=WZ/XY$

Applying means extremes product theorem, we get

  $WS.XY=XS.WZ$