Parallelograms

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Parallelograms
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Parallelogram
Definition
A quadrilateral with both pairs of opposite sides
parallel.

• 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.

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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.
3. Diagonals bisect each other but are not
congruent
P is the midpoint of AC and BD, so BP PD and AP
PC.
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Examples
H
K
M
P
L

• Draw HKLP.
• HK _______ and HP ________ .
• mlt K mlt______ .
• mlt L mlt______ 180.
• If mlt P 65, then mlt H ____, mlt K ____ and
• mlt 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 mltHPK 36, then mltPKL _____ .

PL
KL
P
P or K
115
65
115
5 units
(Alternate interior angles are congruent.)
14 units
7.5 units
36
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Examples

• ABCD is a parallelogram. Find the values of x, y,
  and z.

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Example 2 In GEOM, EA 2x2 5x and AM
4x 2. Find the value of x. What are EA and AM?
G
M
A
E
O
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Example 3. Given TRAC. If TC 3x - 5 and
RA 25, solve for x.
T
R
3
4
K
1
2
If m?CTR 2y - 13 and m?ACT y 1. Find y.
A
C
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Example 4