Chapter 6.2, Problem 16WE

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 rhombus are perpendicular”

The given additional statement is “ $JKLM$ is a rhombus”.

Consider $JKLM$ is a rhombus.

The diagonals are $\overline{JL}\&\overline{KM}$ .

Hence, conclusion is “ $\overline{JL}\perp \overline{KM}$ ”.

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 rhombus are perpendicular”

The given additional statement is “ In quad $DIME$ , $\overline{DM}\perp \overline{IE}$ ”.

Consider $\overline{DM}\perp \overline{IE}$

In quad $DIME$ may or may not be a rhombus.

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 rhombus are perpendicular”

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

Consider $STUV$ is not a rhombus.

The diagonals are may or may not be perpendicular.

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 rhombus are perpendicular”

The given additional statement is “In quad $NOPQ$ , not $\overline{NP}\perp \overline{OQ}$ ”.

Consider $\overline{NP}\&\overline{OQ}$ are not perpendicular.

Hence, the conclusion is “ $NOPQ$ is a not rhombus”.