parallelograms
DESCRIPTION
Parallelograms. B. C. D. A. 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. - PowerPoint PPT PresentationTRANSCRIPT
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Parallelograms
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Parallelogram2
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.
Definition: A quadrilateral with both pairs of opposite sides parallel.
CB
A D
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Properties of Parallelogram
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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.
A B
CDP
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Examples 4
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 = _____ .
H K
LP
PL KLP
P or K
115° 65°
115°
M
5 units
14 units7.5 units
36°
(Alternate interior
angles are congruent.)
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Examples5
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
E
M
O
A
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Example 3. Given TRAC. If TC = 3x - 5 and RA = 25, solve for x.
T R
AC
1
K
43
2
If m CTR = 2y - 13 and m ACT = y + 1. Find y.∠ ∠
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Example 48