Chapter 7.3, Problem 10CE

a.

To determine

To find:The values of $m\angle Y\text{'},m\angle D$

Answer to Problem 10CE

  $m\angle Y\text{'}={70}^0$ and $m\angle D={90}^0$

Explanation of Solution

Given:

Quadrilateral $JUDY\sim J\text{'}U\text{'}D\text{'}Y\text{'}$ .

  

SinceQuadrilateral $JUDY\sim J\text{'}U\text{'}D\text{'}Y\text{'}$

So, $m\angle Y=m\angle Y\text{'}$

  $\Rightarrow m\angle Y\text{'}={70}^0$

And $m\angle D\text{'}=m\angle D$

  $\Rightarrow m\angle D={90}^0$

Conclusion:

Hence, the complete statement is $m\angle Y\text{'}={70}^0$ and $m\angle D={90}^0$ .

b.

To determine

To find:The value of scale factor of quadrilateral.

Answer to Problem 10CE

The scale factor of quadrilateral $JUDY$ to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$ is $\frac{4}{3}$

Explanation of Solution

Given:

Quadrilateral $JUDY$ similar to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$

Given statement: The scale factor of quadrilateral $JUDY$ to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$ is $?$

  

The scale factor of quadrilateral $JUDY$ to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$ is corresponding lengths of quadrilateral $JUDY$ divided by corresponding lengths of quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$ .

  $\Rightarrow \frac{YD}{Y\text{'}D\text{'}}$

  $\Rightarrow \frac{20}{15}$

  $\Rightarrow \frac{4}{3}$

Conclusion:

Therefore, the scale factor of quadrilateral $JUDY$ to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$ is $\frac{4}{3}$ .

c.

To determine

To find:The values of $DU,Y\text{'}J\text{'},J\text{'}U\text{'}$

Answer to Problem 10CE

  $DU=8$ , $Y\text{'}J\text{'}=21$ , and $J\text{'}U\text{'}=9$

Explanation of Solution

Given:

Quadrilateral $JUDY\sim J\text{'}U\text{'}D\text{'}Y\text{'}$

  

  $D\text{'}U\text{'}=6$

Scale factor $=\frac{4}{3}$

Let $DU=x$

So, $DU=6\times \frac{4}{3}$

  $\Rightarrow DU=8$

Now $YJ=28$ ,

Scale factor $=\frac{3}{4}$

Let $Y\text{'}J\text{'}=y$

So, $Y\text{'}J\text{'}=28\times \frac{3}{4}$

  $\Rightarrow Y\text{'}J\text{'}=21$

Now $JU=12$ ,

Scale factor $=\frac{3}{4}$

Let $J\text{'}U\text{'}=z$

So, $J\text{'}U\text{'}=12\times \frac{3}{4}$

  $\Rightarrow J\text{'}U\text{'}=9$

Conclusion:

Therefore, $DU=8$ , $Y\text{'}J\text{'}=21$ , and $J\text{'}U\text{'}=9$ .

d.

To determine

To find: The ratio of the perimeters.

Answer to Problem 10CE

The ratio of the perimeters is $\frac{34}{25}$

Explanation of Solution

Given:

Quadrilateral $JUDY$ similar to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$

  

Perimeter of quadrilateral $JUDY=JU+UD+DY+YJ$

  $\Rightarrow 12+8+20+28$

  $\Rightarrow 68$

Perimeter of quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}=J\text{'}U\text{'}+U\text{'}D\text{'}+D\text{'}Y\text{'}+Y\text{'}J\text{'}$

  $\Rightarrow 9+6+15+21$

  $\Rightarrow 50$

Ratio of perimeters $=\frac{68}{50}$

  $\Rightarrow \frac{34}{25}$

Conclusion:

Therefore, the ratio of the perimeters is $\frac{34}{25}$ .

e.

To determine

To complete the given statement.

Answer to Problem 10CE

To explain: why the given statement is not true.

Explanation of Solution

Given:

Quadrilateral $JUDY$ similar to quadrilateral $J\text{'}U\text{'}D\text{'}Y\text{'}$

Given statement: Explain why it is not true that quadrilateral $DUJY$ is similar to quadrilateral $Y\text{'}J\text{'}U\text{'}D\text{'}$ .

  

The given statement cannot be true because there is no coordination in the corresponding parts.

Conclusion:

Therefore, the given statement cannot be true.