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Chapter 6 Exploring Quadrilaterals

Quadrilateral -

A four sided figure

Examples

Non-Examples

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

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

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

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

Example 2

Given ?1 ? ? 3 and ?2 ? ?4 determine if

quadrilateral ABCD is a parallelogram.

2

1

3

4

Example 3

In the quadrilateral what is the probability that

two randomly chosen angles are congruent?

2

1

Click here for hint

3

4

List all possible solutions

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