1. 4/16/2017
Parallelograms

2. Parallelogram Definition:
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Definition:
A quadrilateral with both pairs of opposite sides parallel. C B A D
The symbol for parallelogram is a smaller version of the figure.
A parallelogram is named using all four vertices.
You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction.
For example, the figure above can be either ABCD or
ADCB.

3. Properties of Parallelogram
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Properties of Parallelogram A B P D C
1. Both pairs of opposite sides are congruent.
2. Both pairs of opposite angles are congruent.
Diagonals bisect each other but are not congruent
P is the midpoint of AC and BD, so BP = PD and AP = PC.

4. 4/16/2017 H
Examples K M P L
Draw HKLP. HK = _______ and HP = ________ . m< K = m<______ . m< L + m<______ = 180°. If m< P = 65°, then m< H = ____, m< K = ____ and m< L =____. Draw the diagonals with their point of intersection labeled M. If HM = 5, then ML = ____ . If KM = 7, then KP = ____ . If HL = 15, then ML = ____ . If m<HPK = 36°, then m<PKL = _____ . PL KL P
P or K
115°
65°
115°
5 units
(Alternate interior
angles are congruent.)
14 units
7.5 units
36°

5. Examples ABCD is a parallelogram. Find the values of x, y, and z.
4/16/2017
Examples
ABCD is a parallelogram. Find the values of x, y, and z.

6. Example 2: In GEOM, EA = 2x2 + 5x and AM = 4x + 2. Find the value of x
Example 2: In GEOM, EA = 2x2 + 5x and AM = 4x Find the value of x. What are EA and AM? G M A E O

7. Example 3. Given TRAC. If TC = 3x - 5 and RA = 25, solve for x.4 K 1 2
If m∠CTR = 2y - 13 and m∠ACT = y + 1. Find y. C A

8. Example 4