Chapter 9, Problem 13CUR

a)

To determine

To write: the contrapositive of the given statement.

Answer to Problem 13CUR

If $\angle A\ne \angle C$ then quadrilateral $ABCD$ is not a parallelogram.

Explanation of Solution

Given information:

Given statement,

If quad. $ABCD$ is a parallelogram, then $\angle A\cong \angle C$ .

Calculation:

Consider the following statement:

If a quadrilateral $ABCD$ is parallelogram, then $\angle A\cong \angle C$ .

The contra positive of the above statement is given by. “If $\angle A\ne \angle C$ then quadrilateral $ABCD$ is not a parallelogram”.

b)

To determine

To write: the inverse of the given statement.

Answer to Problem 13CUR

If quadrilateral $ABCD$ is not a parallelogram then $\angle A\ne \angle C$ .

Explanation of Solution

Given information:

Given statement,

If quad. $ABCD$ is a parallelogram, then $\angle A\cong \angle C$ .

Calculation:

Consider the following statement:

If a quadrilateral $ABCD$ is parallelogram, then $\angle A\cong \angle C$ .

The inverse of the above statement is given by. “If quadrilateral $ABCD$ is not a parallelogram then $\angle A\ne \angle C$ ”