Chapter 6 Exploring Quadrilaterals

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Chapter 6 Exploring Quadrilaterals
Quadrilateral -
A four sided figure
Examples
Non-Examples
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1 Type of Quadrilateral
Both pair of opposite sides parallel
Parallelogram-
N
M
What conjectures can you make about the sides of
MNPG and the angles of the parallelogram?
Q
P
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Theorem 6-1 Opposite sides of a parallelogram
are congruent
Theorems
Theorem 6-2 Opposite angles of a parallelogram
are congruent
Theorem 6-3 Consecutive angles in a
parallelogram are supplementary
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All polygons with more than 3 sides have diagonals
Segments that connect any two nonconsecutive
vertices.
Diagonal-
Theorem 6-4 The diagonals of a parallelogram
bisect each other
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Example 1
WXYZ is a parallelogram, m?ZWX b, and m?WXY
d. Find the values of a, b, c, and d.
W
X
2c
15
a
18?
31?
Y
Z
22
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Example 2
Given ?1 ? ? 3 and ?2 ? ?4 determine if
quadrilateral ABCD is a parallelogram.
2
1
3
4
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Example 3
In the quadrilateral what is the probability that
two randomly chosen angles are congruent?
2
1
Click here for hint
3
4
8
List all possible solutions