1. Properties of Parallelograms
Chapter 6 Section 6.2
Properties of Parallelograms

2. Transitive
Symmetric
Substitution

3. Some Properties of Parallelograms
Definition
Definition Parallelogram
A parallelogram is quadrilateral with both pairs of
opposite sides parallel

4. No, Only one pair of opposite sides are parallel
Some Properties of Parallelograms
No, Only one pair of opposite sides are parallel
Yes, both pairs of opposite sides are parallel

5. No, The polygon is a hexagon
Some Properties of Parallelograms
No, The polygon is a hexagon

6. Some Properties of Parallelograms
Theorem
Theorem 6.2
If a quadrilateral is a parallelogram, then both pairs
of opposite sides are congruent

7. W  Y and X  Z Some Properties of Parallelograms Theorem
If a quadrilateral is a parallelogram, then both pairs
of opposite angles are congruent
W  Y and X  Z

8. mW + mX = 180 mX + mY = 180 mY + mZ = 180 mZ + mW = 180
Some Properties of Parallelograms
Theorem
Theorem 6.4
If a quadrilateral is a parallelogram, then consecutive
angles are supplementary
mW + mX = 180
mX + mY = 180
mY + mZ = 180
mZ + mW = 180

9. KJGH with diagonals Some Properties of Parallelograms Theorem
If a quadrilateral is a parallelogram, then its diagonals
bisect each other
KJGH with diagonals

10. = 10.15 = 13 = XO + ON = 3 + 3 = 6 = KP + PX + XR = PX = XR = 5
Some Properties of Parallelograms
= 13
= 10.15
= XO + ON
= 3 + 3
= 6
= KP + PX + XR =
= 15
= LX +XN
= 6 + 6
=12
= PX = XR = 5

11. = mKLN = 68.3 = 50.7 = mNKL = 61 = 68.3 = KN + NM + LM + KL
Some Properties of Parallelograms
= mKLN
= 68.3
= 50.7
= mNKL
= 61
= 68.3
= KN + NM + LM + KL =
= 46.3

12. Opposite sides are congruent
Some Properties of Parallelograms
Opposite sides are congruent
5x = 3x + 18
2x = 18
x = 9
3y – 7 = 2y + 4
y – 7 = 4
y = 11

13. Opposite angles are congruent
Some Properties of Parallelograms
Opposite angles are congruent
3x – 18 = 2x + 12
x – 18 = 12
x = 30
Consecutive angles are Supplementary
4y + 72 = 180
4y = 108
y = 27
3z + 72 = 180
3z = 108
z = 36
2(30) + 12 72

14. Diagonals Bisect Each Other
Some Properties of Parallelograms
Diagonals Bisect Each Other
7y – 2 = 5y + 4
2y – 2 = 4
2y = 6
y = 3
3x + 2 = 23
3x = 21
x = 7

15. Applications of Parallelogram Properties

16. Applications of Parallelogram Properties

17. HW #67 Pg