Question

What theorem in this section is the converse of each theorem?

1. Theorem 5-1
2. Theorem 5-2
3. Theorem 5-3

Short answer

1. The converse of the theorem 5-1 is the theorem 5-4 which states that if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.
2. The converse of the theorem 5-2 is the theorem 5-6 which states that if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.
3. The converse of the theorem 5-3 is the theorem 5-7 which states that if the diagonals of the quadrilateral bisect each other then the quadrilateral is a parallelogram.

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.  Definition of converse of theorem.

The statement that can be formed by interchanging the given section of a theorem with what to prove section of the theorem is converse of the theorem.

Step 3.  Write the converse of the theorem 5-1.

The converse of the theorem 5-1 is the theorem 5-4 which states that if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.

Step 1.  Write the theorem 5-2.

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

Step 2.  Definition of converse of theorem.

The statement that can be formed by interchanging the given section of a theorem with what to prove section of the theorem is converse of the theorem.

Step 3.  Write the converse of the theorem 5-2.

The converse of the theorem 5-2 is the theorem 5-6 which states that if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.

Step 1.  Write the theorem 5-3.

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

Step 2.  Definition of converse of theorem.

The statement that can be formed by interchanging the given section of a theorem with what to prove section of the theorem is converse of the theorem.

Step 3.  Write the converse of the theorem 5-3.

The converse of the theorem 5-3 is the theorem 5-7 which states that if the diagonals of the quadrilateral bisect each other then the quadrilateral is a parallelogram.