Question

State each theorem in if-then form. (Begin “ If a quadrilateral is a …”)

a. Theorem 5-1 b. Theorem 5-2 c. Theorem 5-3

Short answer

a.The theorem 5-1 in if-then form is if a quadrilateral is a parallelogram then the opposite sides of the quadrilateral are congruent.

b. The theorem 5-2 in if-then form is if a quadrilateral is a parallelogram then the opposite angles of the quadrilateral are congruent.

c. The theorem 5-3 in if-then form is if a quadrilateral is a parallelogram then the diagonals of the quadrilateral bisect each other.

Step-by-step solution

Step 1.  Write the theorem 5-1.

The theorem 5-1 states that opposite sides of a parallelogram are congruent.

Step 2.  Description of step.

If a statement is written in if-then form then after the word ‘if’ the condition is written and after the word ‘then’ the result is written.

Step 3.  State the theorem 5-1 in if-then form.

The theorem 5-1 in if-then form is if a quadrilateral is a parallelogram then the opposite sides of the quadrilateral are congruent.

Step 1.  Write the theorem 5-2.

The theorem 5-2 states that opposite angles of a parallelogram are congruent.

Step 2.  Description of step.

If a statement is written in if-then form then after the word ‘if’ the condition is written and after the word ‘then’ the result is written.

Step 3.  State the theorem 5-2 in if-then form.

The theorem 5-2 in if-then form is if a quadrilateral is a parallelogram then the opposite angles of the quadrilateral are congruent.

Step 1.  Write the theorem 5-3.

The theorem 5-3 states that diagonals of a parallelogram bisect each other.

Step 2.  Description of step.

If a statement is written in if-then form then after the word ‘if’ the condition is written and after the word ‘then’ the result is written.

Step 3.  State the theorem 5-3 in if-then form.

The theorem 5-3 in if-then form is if a quadrilateral is a parallelogram then the diagonals of the quadrilateral bisect each other.