Download Chapter 7 Parallelogram

Chapter 7
7.2 Properties of Parallelograms
7.3 Proving Quadrilateral are Parallelograms
Parallelogram
Quadrilateral with two pairs of parallel sides.
Parallelogram Properties
If a quadrilateral is a parallelogram then…
­ Opposite sides are congruent
­ Opposite angles are congruent
­ Consecutive angles are supplementary
­ Diagonals Bisect each other
Examples
Given: JKLM is a parallelogram, ∠K=115, JK = 10, Perimeter = 30, JN = 6, and MN = 7 Find ∠J, ∠M, ∠L, ML, JM, KL, NL, KN
Example
(?, ?)
(15, 7)
(11, 0)
(0, 0)
Example
(?, ?)
(0, 0)
(2j, 2k)
(2h, 0)
Prove a Parallelogram
A quadrilateral is a parallelogram if one of the following is true …
­ Opposite sides are congruent (distance 4 times)
­ Opposite angles are congruent ­ Consecutive angles are supplementary ­ Diagonals bisect each other (midpt. twice)
­ One pair of opposite sides are congruent and parallel (distance twice and slope twice)
1. Both sets of opposite angles are congruent
2. Both sets of opposite sides are congruent
3. Diagonal bisect each other
4. One pair of opposite sides are congruent and parallel
5. One pair of opposite sides are congruent and parallel (Alt. Int. Angles)
6. Diagonals bisect each other
7. Both sets of opposite angles are congruent
8. NOT a parallelogram
Is the quadrilateral a parallelogram? Prove your answer algebraically.
W(­6, 5) X(1, 3) Y(3, ­4) Z(­4, ­2)
Homework
• Pg. 381 #13­37
• Pg. 387­388 #16­30 evens and #34