Chapter 5.1, Problem 16CE

a)

To determine

To find: The statement of theorem 5.1 in IF-THEN form.

Answer to Problem 16CE

Statement of theorem 5.1 in IF-THEN form is written as,” IF a quadrilateral is a parallelogram THEN its opposite sides are congruent.”

Explanation of Solution

Given information: Statements of following theorem is given,

Theorem 5.1: “Opposite sides of a parallelogram are congruent.’

In IF-THEN statement, condition given is written under IF and its result is written under THEN section. So, its formal is, “IF THEN < Result>.”

Thus, the statement of theorem 5.1 should be written as, “IF a quadrilateral is a parallelogram THEN its opposite sides are congruent.”

Conclusion: Thus, above is the required IF-THEN statement equivalent to statement of theorem 5.1.

b)

To determine

To find: The statement of theorem 5.2 in IF-THEN form.

Answer to Problem 16CE

Statement of theorem 5.2 in IF-THEN form is written as,” IF a quadrilateral is a parallelogram THEN its opposite angles are congruent.”

Explanation of Solution

Given information: Statements of following theorem is given,

Theorem 5.2: “Opposite angles of a parallelogram are congruent.’

In IF-THEN statement, condition given is written under IF and its result is written under THEN section. So, its formal is, “IF THEN < Result>.”

Thus, the statement of theorem 5.2 should be written as, “IF a quadrilateral is a parallelogram THEN its opposite angles are congruent.”

Conclusion: Thus, above is the required IF-THEN statement equivalent to statement of theorem 5.2.

c)

To determine

To find: The statement of theorem 5.3 in IF-THEN form.

Answer to Problem 16CE

Statement of theorem 5.3 in IF-THEN form is written as,” IF a quadrilateral is a parallelogram THEN its diagonals bisect each other.”

Explanation of Solution

Given information: Statements of following theorem is given,

Theorem 5.3: ”Diagonals of a parallelogram bisect each other.”

In IF-THEN statement, condition given is written under IF and its result is written under THEN section. So, its formal is, “IF THEN < Result>.”

Thus, the statement of theorem 5.3 should be written as, “IF a quadrilateral is a parallelogram THEN its diagonals bisect each other.”

Conclusion: Thus, above is the required IF-THEN statement equivalent to statement of theorem 5.3.