Chapter 6.2, Problem 15WE

a)

To determine

To write: the conclusion of the given statement with additional statement.

Explanation of Solution

Given information:

The given statement is “If two angles are vertical angles, then they are congruent"

The given additional statement is “ $\angle 1\cong \angle 2$ ”

Consider $\angle 1\cong \angle 2$ , but they may or may not be vertical angles.

Hence, conclusion is not possible.

b)

To determine

To write: the conclusion of the given statement with additional statement.

Explanation of Solution

Given information:

The given statement is “If two angles are vertical angles, then they are congruent"

The given additional statement is “ $m\angle ABC\ne m\angle DBF$ ”

Consider $m\angle ABC\ne m\angle DBF$

Vertical angles are congruent.

Hence, the conclusion is “ $\angle ABC\&\angle DBF$ are not vertical angles”.

C)

To determine

To write: the conclusion of the given statement with additional statement.

Explanation of Solution

Given information:

The given statement is “If two angles are vertical angles, then they are congruent"

The given additional statement is “ $\angle 3\&\angle 4$ are adjacent angles”

The adjacent angles may or may not be congruent..

Hence, there is no conclusion possible.

d)

To determine

To write: the conclusion of the given statement with additional statement.

Explanation of Solution

Given information:

The given statement is “If two angles are vertical angles, then they are congruent"

The given additional statement is “ $\overline{RS}\&\overline{TU}$ are intersect at V.”

Consider $\overline{RS}\&\overline{TU}$ are intersect at V.

  $\angle RVT$ and $\angle SVU$ are vertical angles and they are congruent.

Hence, the conclusion is “ $\angle RVT\cong \angle SVU.$