Chapter 8.5, Problem 13PSA

To determine

To find the value of two sides.

Answer to Problem 13PSA

The value of QZ is 2.45 and ZY is 6.48

Explanation of Solution

Given information:

r is parallel to s.

s is parallel to t.

  $\begin{array}{l}WV=3,\\ WX=8,\\ QY=9\end{array}$

Formula used:

The below properties are used:

If the lines are parallel then their corresponding angles are congruent.

Corresponding sides of similar quadrilateral are proportional.

Calculation:

  

It is given that,

r is parallel to s. s is parallel to t.

  $\begin{array}{l}WV=3,\\ WX=8,\\ QY=9\end{array}$

If the lines are parallel then their corresponding angles are congruent.

  $\begin{array}{l}\angle Z\cong \angle Y\\ \angle W\cong \angle X\end{array}$

By AA similarity rule, we get

  $▱VWZQ~▱VXYQ$

Corresponding sides of similar quadrilateral are proportional.

  $\begin{array}{l}\frac{QZ}{ZY}=\frac{WV}{WX}\\ \frac{QZ}{ZY}=\frac{3}{8}\\ 3x+8x=9\\ 11x=9\\ x=\frac{9}{11}\\ QZ=3x\\ =3*0.81\\ =2.45\\ ZY=8x\\ =8*0.81\\ =6.48\end{array}$