1. Lesson 61 Determining if a Quadrilateral is a Parallelogram
Properties of sides, diagonals and angles of parallelograms.

2. What are some properties of parallelograms?
From Lesson 34 we learned:
Opposite sides parallel
Opposite sides congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other

3. “Converse” of Lesson 34
You will be using the converse of some of those properties to prove if a quadrilateral is a parallelogram.

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

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

6. Find x, y, & z that would make ABCD a parallelogram.
8𝑥−70=3𝑥+5 5𝑥=75 𝑥=15 7𝑦=9𝑦−32 −2𝑦=−32 𝑦= 𝑧= 𝑧=180 4𝑧=68 𝑧=17

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

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

9. Is quadrilateral JKLM a parallelogram?
5𝑥−24=26 5𝑥=50 x= = = −5= =35 Yes, diagonals bisect each other.

10. Remember use these properties to prove a quadrilateral is a parallelogram
Opposite sides congruent
Opposite angles congruent
Diagonals bisect each other
One pair parallel & congruent
Any questions?