Theorem 5-4 to 5-7 + 5 ways...

Question 1

Theorem 5-4

Answer 1

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Question 2

Theorem 5-5

Answer 2

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Question 3

Theorem 5-6

Answer 3

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Question 4

Theorem 5-7

Answer 4

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Question 5

List the 5 ways to prove a Quadrilateral is a Parallelogram

Answer 5

1. Show that both pairs of opposite sides are parallel
2. Show that both pairs of opposite sides are congruent
3. Show that one pair of opposite sides are both congruent and parallel
4. Show that both pairs of opposite angles are congruent
5. Show that the diagonals bisect each other