Chapter 8.6, Problem 46E

(a)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

True

Explanation of Solution

Given: $\overline{CA}\cong \overline{AF}$

  

  $\overline{CA}\cong \overline{AF}$

The statement is true as it is given in the figure.

(b)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

True

Explanation of Solution

Given: $C,A,F$ are collinear.

  

  $C,A,F$ are collinear.

The statement is true as they all lie in a same line.

(c)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

Not true

Explanation of Solution

Given: $\angle CAD\cong \angle EAF$

  

  $\angle CAD\cong \angle EAF$

The statement is not true.

(d)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

True

Explanation of Solution

Given: $\overline{BA}\cong \overline{AE}$

  

  $\overline{BA}\cong \overline{AE}$

The statement is true.

  $\begin{array}{l}\angle BAD=90\\ ADistransversal\\ \angle BAD+\angle EAD=180\\ 90+\angle EAD=180\\ \angle EAD=90\\ \overline{BA}\cong \overline{AE}\end{array}$

(e)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

True

Explanation of Solution

Given: $\overline{CF},\overline{BE},\overline{AD}$ intersect at point $A.$

  

  $\overline{CF},\overline{BE},\overline{AD}$ has the common point $A.$

The statement is true.

(f)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

True

Explanation of Solution

Given: $\angle BACand\angle CAD$ are complementary angles.

  

  $\angle BACand\angle CAD$ are complementary angles.

  $\begin{array}{l}\angle BAC+\angle CAD=\angle BAD\\ \angle BAC+\angle CAD=90\end{array}$

The statement is true.

(g)

To determine

To Find: The statement given is true or false based on the figure.

Answer to Problem 46E

True

Explanation of Solution

Given: $\angle DAE$ is a right angle.

  

  $\angle DAE$ is a right angle.

The statement is true.

  $\begin{array}{l}\angle BAD=90\\ ADistransversal\\ \angle BAD+\angle EAD=180\\ 90+\angle EAD=180\\ \angle DAE=90\end{array}$