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Geo.4.16.15.sec.9.2.notebook April 16, 2015
Prove Theorem 9-1
Opposite sides of a parallelogram are congruent.
A
B C
D1 2
3 4
Given: ABCD
Prove: AB CD, BC ADstatements reasons
WARM UP
AB II CD
Hw Solutions p. 451 # 1-10, 17-22
1.
62°1 2
3
2.
1 23
110°38°
71°28°
1 2 3
3.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
12
385°48°
4.5.
32
15
A
EB
P
Find AP.
6. YP = 8, TR = 10
Y
T P
R
A
7. YP = 8, TR = 10
A
TY
R
P
8. MD = ½ ADA
P
M
D42
Find AP.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
9. The perimeter of parallelogram RSTW is 48 cm. If RS = 17, find the lengths of the other sides of the parallelogram.
10. The perimeter of parallelogram EFGH is 48 in. If EF is 5 in less than EH, find the lengths of the other sides of the parallelogram.
17.
60 2x x
18.
y
3y 3x
19.
x z 5
71 y + 21
20.y + 16 2x 1
x + 24
Geo.4.16.15.sec.9.2.notebook April 16, 2015
21.
x y
x + y
3y 6
22.
y 3y 8
x 2
2x 12
REVIEWName 5 properties of parallelograms.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
92 Conditions for Parallelograms
We have learned the properties of a parallelogram. Now we will be given the properties of a quadrilateral
and will have to tell if the quadrilateral is a parallelogram.
To do this, we willuse the definition of a parallelogram
or the following conditions.
Definition of a parallelogram:
p. 454
Theorem 95
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
Theorem 96
If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
Theorem 97
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
Theorem 98
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Determine if the quadrilateral must be a parallelogram. Justify your answer.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
Show that JKLM is a parallelogram for a = 3 and b = 9.
Show that PQRS is a parallelogram for x = 10 and y = 6.5.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
Show that PQRS is a parallelogram for a =
2.4 and b = 9.
You have learned several ways to determine whether a quadrilateral is a parallelogram. You can use the given information about a figure to
decide which condition is best to apply.
To show that a quadrilateral is a parallelogram, you only have to show that it satisfies one of these sets of conditions.
Geo.4.16.15.sec.9.2.notebook April 16, 2015
HW # 94p. 45758 # 1 14, 18 21