1. Properties of Parallelograms
Lesson 7.2
Properties of Parallelograms

2. Essential Question: What are the properties of parallelograms?

3. Parallelogram
A quadrilateral with two pairs of opposite sides that are parallel.
Symbol
We could write “parallelogram ABCD”.
Or, we could use the symbol and write “ ABCD”.
Or, “Pgram ABCD”.

4. Theorem 7.3 Parallelogram Opposite Sides Theorem
In a parallelogram, opposite sides are congruent.

5. Example 1
Solve for x and y. 4x + 10 = 42 4x = 32 x = 8 2y – 12 = 20 2y = 32 y=16

6. Theorem 7.4 Parallelogram Opposite Angles Theorem
In a parallelogram, the opposite angles are congruent.

7. Find the values of x and y.
Example 2
Find the values of x and y.
2x = 50
x = 25
y + 3 = 18
y= 15

8. Theorem 7.5 Parallelogram Consecutive Angles Theorem
In a parallelogram, consecutive angles are supplementary.

9. Example 3
Solve for x.
3x = 180
3x = 60
x = 20

10. 7.6 Parallelogram Diagonals Theorem
The diagonals of a parallelogram bisect each other.

11. Application
Solve for x. 5x – 8 = 2x x = 2x x = 18 x = 6

12. These properties must be memorized.
In a Parallelogram…
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
These properties must be memorized.
November 27, 2018November 27, 2018

13. Write a two-column proof.
Given ABCD and GDEF are parallelograms Prove
Statements_______________
Reasons_____________ Given
ABCD and GDEF are parallelograms
2. Parallelogram Opp Angles Theorem 2. 3.
3. Vertical Angles Thm
4. Transitive Prop. 4.