Chapter 6.5, Problem 16E

a.

To determine

To explain: If the given information is enough to find $EF$ and $FD$ .

Answer to Problem 16E

The given information is enough to find $EF$ and $FD$

Explanation of Solution

Given information:

  $△ABC\sim △DEF$

  $AB,BC,CA$ and $DE$ is known.

To find $EF$ and $FD$ , write and solve a proportion.

For $EF$ :

  $\frac{AB}{DE}=\frac{BC}{EF}$

Since $AB,DE$ and $BC$ are known, $EF$ can be calculated.

For $FD$ :

  $\frac{AB}{DE}=\frac{CA}{FD}$

Since $AB,CA$ and $DE$ are known, $FD$ can be calculated.

Therefore, the given information is enough to find $EF$ and $FD$ .

b.

To determine

To explain: If the given information is enough to find $CA$ .

Answer to Problem 16E

The given information is not enough to find $CA$ .

Explanation of Solution

Given information:

  $△ABC\sim △DEF$

  $AB,BC$ and $FD$ is known.

To find $CA$ , write and solve a proportion.

  $\frac{AB}{DE}=\frac{CA}{FD}$

Since $DE$ and $CA$ are unknown, $FD$ cannot be calculated.

c.

To determine

To explain: If the given information is enough to find $m\angle E$ .

Answer to Problem 16E

The given information is enough to find $m\angle E$ .

Explanation of Solution

Given information:

  $△ABC\sim △DEF$

  $m\angle B$ is known.

To find $m\angle E$ , use properties of similar figures. For two similar figures, the corresponding sides are congruent. $\angle B$ is corresponding to $\angle E$ .

Therefore,

  $\angle B\cong \angle E$

As $m\angle B$ is known $m\angle E$ can be calculated.