1. 7.1 Properties of Parallelograms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

2. Theorem 7-1-1
If a quadrilateral is a parallelogram, then its opposite sides are congruent.

3. Example Find BD Find CD Find BE Find m<ABC Find m<ADC
The picture below is a parallelogram. In ABCD, AB = 17.5, DE=18, and m<BCD = 110°. B C
Find BD
Find CD
Find BE
Find m<ABC
Find m<ADC
Find m<DAB E A D

4. Example 1 a) b) Y – 5 = 22 2x – 5 = 11 3x = 18 9x +1 = 28 + 5 = +5
X = 6
Y – 5 = 22
+ 5 = +5
Y = 27
2x – 5 = 11
+ 5 = +5
2x = 16
x = 8
9x +1 = 28
- 1 = - 1
9x = 27
x = 3

5. Theorem 7-1-2
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

6. Examples ABCD is a parallelogram. Find the m<B. C B (7y + 5)°

7. Example 2 a) b) (7x – 10)° (7x – 1)° 139° (6x – 1)° (7x – 1)° = 139°
+ 1 = +1
(7x)° = 140°
(7x)° = 140°
x =
(7x – 10)° = (6x – 1)°
-6x = -6x
x – = -1
= +10
x = 9

8. Consecutive Angles
Angles of a polygon that share a side are consecutive angles.

9. Theorem 7-1-3
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

10. Using Consecutive Angles
What is the measure of angle P in parallelogram PQRS?
26°
64°
116°
126°

11. Example 3 a) b) 120° (5x+20)° (8y +4)° 9x° 135° 9x° + 135° = 180°
-135 = -135
9x° = 45°
9x = 45
x = 5
(5x+20)° + 120° = 180°
5x° + 140° = 180°
= -140
5x° = 40°
5x = 40
x = 8
(8y+4)° + 120° = 180°
8y° + 124° = 180°
= -140
8y° = 56°
8y = 56
x = 7

12. Theorem 7-1-4
If a quadrilateral is a parallelogram, then its diagonals bisect each other.

13. Example Find b Find a b+8 = 5b 3a – 7 = 2a -b = -b + 7 = + 7 8 = 4b
b = 2
Find a
3a – 7 = 2a
+ 7 =
3a = 2a + 7
-2a = -2a
a = 7

14. Example 4 Find x 5x – 1 = 14 + 1 = +1 5x = 15 5x = 15 5 5 x = 3 Find y18
5x - 1 14 9y b)
7y + 2
5x-8
10y - 7
4x + 4
Find x
5x – 1 = 14
+ 1 = +1
5x = 15
5x = 15
x = 3
Find y
9y = 18
9y = 18
y = 2
Find x
5x – 8 = 4x +4
-4x = -4x
x = 4
+8 = +8
x = 12
Find y
10y – 7 = 7y + 2
-7y = -7y
3y – 7 = 2
+7 = +7
3y = 9
3y = 9
y = 3