Download Unit VIII – Quadrilaterals pg.1 Geometry Name Quadrilaterals 1

Geometry
Quadrilaterals
Name __________________
SOME WARM-UP QUESTIONS:
1.
How do you know if a figure is a quadrilateral?
2.
How many degrees are there in all the angles of a quadrilateral?
3.
What quadrilateral has one, and only one, pair of opposite sides that are parallel?
4.
What quadrilateral has both pairs of opposite sides that are parallel?
What is true about the lengths of those opposite pairs of sides?
5.
What quadrilateral is just like the quadrilateral in #4, except that all the angles are
right angles?
6.
What quadrilateral is just like the quadrilateral in #5, except that all of the sides of
the quadrilateral are the same length?
7.
What quadrilateral is just like the quadrilateral in #6, except that the angles are
NOT right angles?
Unit VIII – Quadrilaterals
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PROPERTIES OF PARALLELOGRAMS:
First, let’s draw and name all the different kinds of shapes that fit into the category of
parallelograms:
(a)
(b)
(c)
(d)
Below are two things that are true about parallelograms, all parallelograms:
1.
Both pairs of _________________________________ of a parallelogram
are ____________________________.
2.
Both pairs of _________________________________ of a parallelogram
are ____________________________.
Unit VIII – Quadrilaterals
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Example 1 Find the measures of < A and < B:
B
A
120°
60°
D
C
Example 2 First find x, and then find the measure of each angle:
A
x = __________
B
x – 15
2x
< A = __________
< B = __________
< C = __________
D
C
< D = __________
Example 3 Find the measures of < A and < B:
B
A
27°
C
Unit VIII – Quadrilaterals
153°
D
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Example 4 First find x, and then find the measure of each angle:
A
2x
x = __________
B
< A = __________
x
C
< B = __________
D
< C = __________
< D = __________
THE PERIMETER OF A SHAPE:
Definition:
Example 5 Find the perimeter of each of these parallelograms:
B
A
A
10
B
7
C
8
18
Unit VIII – Quadrilaterals
D
C
D
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Below is a third property that is true of all parallelograms:
3.
Consecutive _________________________________ of a parallelogram
are ____________________________ which means they add to ______________.
Example 6 Find the measures of < A and < B and < D:
B
A
32°
D
C
And below is the fourth, and last, property of all parallelograms:
4.
The diagonals of a parallelogram _______________________ each other,
which means that they divide each other into ______________ segments.
Example 7
If RSTU is a parallelogram and RV = 12 and SV = 13, then find the
length of each diagonal.
S
R
RT = __________
V
SU = __________
U
Unit VIII – Quadrilaterals
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Example 8 Find the measures of < A and < B and < C:
B
A
112°
C
D
Example 9
If ABCD is a parallelogram and AC = 14 and BD = 8, then find the
lengths of AE, BE, CE, and DE:
AE = __________
B
A
BE = __________
E
CE = __________
D
C
DE = __________
--------------------------------------------------------------------------------------------EXERCISES: page 276–278 (1 – 18 all)
Unit VIII – Quadrilaterals
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