Chapter 8.5, Problem 1PSA

Solution

a.

To calculate: The measure of ED.

The measure of ED is $8$

Given: BE is parallel to CD

Concept used: Here, we are using angle angle similarity rule.

Calculation: In $\Delta EAB$ and $\Delta DAC$

So, $\angle A=\angle A$ (common)

And, $\angle AEB=\angle ADC$ (corresponding angles)

So, $\Delta EAB\sim \Delta DAC$ (by angle angle similarity)

Hence, $\frac{AB}{BC}=\frac{AE}{ED}$

➔ $\frac{3}{4}=\frac{6}{ED}$

➔ $ED=8$

Conclusion: Hence, the measure of ED is $8$

b.

To calculate: The measure of CD.

The measure of CD is $6.67$

Given: BE is parallel to CD

Concept used: Here, we are using angle angle similarity rule.

Calculation: Here, we can say that,

  $\frac{AB}{BC}=\frac{EB}{DC}$ ( $\because$$\Delta EAB\sim \Delta DAC$ )

➔ $\frac{3}{4}=\frac{5}{CD}$

➔ $CD=\frac{20}{3}=6.67$

Conclusion: Hence, the measure of CD is $6.67$