Chapter 6.2, Problem 17WE

a)

To determine

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

Explanation of Solution

Given information:

The given statement is “The diagonals of the rectangle are congruent"

The given additional statement is “ $PQRS$ is a rectangle”.

Consider $PQRS$ is a rectangle.

The diagonals $\overline{PR}\&\overline{QS}$ are congruent.

Hence, conclusion is “ $\overline{PR}\perp \overline{QS}$ .

b)

To determine

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

Explanation of Solution

Given information:

The given statement is “The diagonals of the rectangle are congruent"

The given additional statement is “ In quad $ABCD$ , $AC=BD$ ”.

Consider $AC=BD$

Diagonals are congruent.

The quad $ABCD$ may or may not be a rectangle.

Hence, the no conclusion is possible.

C)

To determine

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

Explanation of Solution

Given information:

The given statement is “The diagonals of the rectangle are congruent"

The given additional statement is “ $WXYZ$ is not a rhombus”.

Consider $WXYZ$ is not a rectangle

The diagonals are may or may not be congruent.

Hence, conclusion is not possible.

d)

To determine

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

Explanation of Solution

Given information:

The given statement is “The diagonals of the rectangle are congruent"

The given additional statement is “In quad $STAR$ , $SA>TR$ ”.

Consider $SA>TR$

The diagonals are not congruent.

Hence, the conclusion is “ $STAR$ is a not a rectangle”.