1. 6-2 Properties of Parallelograms page 294
Objective: To use relationships among sides, angles, diagonals or transversals of parallelograms.

2. Vocabulary Consecutive angles – angles of a polygon that share a side.
NOTE: Consecutive angles of a parallelogram are supplementary. A B C D

3. You can use what you know about parallel lines & transversals to prove some theorems about parallelograms
Theorem 6.1 p Opposite sides of a parallelogram are congruent

4. Theorem 6-1 Opposite sides of a parallelogram are congruent. AB = DC
AD = BC A B D C

5. Properties of Parallelograms
Use KMOQ to find m O.
Q and O are consecutive angles of
KMOQ, so they are supplementary.
Definition of supplementary angles
m O + m Q = 180
Substitute 35 for m Q.
m O + 35 = 180
Subtract 35 from each side.
m O = 145
6-2

6. Theorem 6-2 Opposite angle of a parallelogram are congruent.
<A = <C
<B = <D A B D C

7. Find the value of x in ABCD. Then find m A.
x + 15 = 135 – x
Opposite angles of a are congruent.
2x + 15 = 135
Add x to each side.
2x = 120
Subtract 15 from each side.
x = 60
Divide each side by 2.
Substitute 60 for x.
m B = = 75
Consecutive angles of a
parallelogram are supplementary.
m A + m B = 180
m A + 75 = 180
Substitute 75 for m B.
Subtract 75 from each side.
m A = 105
6-2

8. Theorem 6-3
The diagonals of a parallelogram bisect each other.

9. Properties of Parallelograms
Find the values of x and y in KLMN.
x = 7y – 16
The diagonals of a parallelogram
bisect each other.
2x + 5 = 5y
2(7y – 16) + 5 = 5y
Substitute 7y – 16 for x in the
second equation to solve for y.
14y – = 5y
Distribute.
14y – 27 = 5y
Simplify.
–27 = –9y
Subtract 14y from each side.
3 = y
Divide each side by –9.
x = 7(3) – 16
Substitute 3 for y in the first
equation to solve for x.
x = 5
Simplify.
So x = 5 and y = 3.
6-2

10. Theorem 6-4
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
BD = DF A B C D E F

11. Closure
Lesson 6-1 defined a rectangle as a parallelogram with four right angles. Explain why you can now define a rectangle as a parallelogram with one right angle.

12. Summary What is true about the opposite sides of a parallelogram?
What is true about the opposite angles of a parallelogram? What about consecutive angles?
What about the diagonals of a parallelogram?
When 3 or more parallel lines cut of congruent segments on one transversal, what is true about all other transversals?

13. Assignment 6.2
Page 297
#2-32 E, 34, 35, 39-41