Post on 26-Mar-2015
Lesson 8.2Lesson 8.2
Definition: A 4-sided shape with parallel opposite sides
Opposite sidesare congruent
Opposite angles are congruent
Consecutive angles are supplementary
a
ab
b
Diagonals bisect each otherEach Diagonal separates
the parallelogram into two congruent triangles
Properties of parallelograms
a + b = 180o
Pg. 415 – 416: #(16 – 31) all
Practice and apply:
Complete each statement about ABCD, Justify your answer
A B
C D
G
Q # 16 – 21
CDA Alternate interior angles
CD Opposite sides of parallelogram are //
ACD Diagonal AD separates the Parallelogram into two congruent triangles
ACDOpposite angles of parallelogram are congruent
CG Diagonals of parallelogram bisect each other
ABD Opposite angles of parallelogram are congruent
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?MNPm22)
RNPmMNRmMNPm
3833MNPm
Alternate interior with MRN
71MNPm
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?NRPm23)
MNRmNRPm
33NRPm
Alternate interior angles
33
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?RNPm24)
MRNmRNPm
38RNPm
Alternate interior angles
33
38
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?RMNm25)
180MNPmRMNm Consecutive angles of parallelogram are supplementary
33
38
18071RMNm
109RMNm
109
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?MQNm26)
180NQPmMQNm Linear pair angles
33
38
18083MQNm
97MQNm
109
97
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?MQRm27)
NQPmMQRm Vertical angles
33
38
83MQRm
109
9783
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?x28)
2043 x Opposite sides of parallelogram are congruent
243 x
8x
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?y29)
9.1752 y Opposite sides of parallelogram are congruent
9.122 y
45.6y
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?w30)
1.1134 w Diagonals of parallelogram bisect each other
1.144 w
525.3w
Practice and apply:
Use MNPR to find each measure or value M N
R P
Q
20
17.9
15.4
3z – 3
4w – 3
11.1
3x – 4
83o
38o
33o
2y + 5
Q # 22 – 31
?z31)
4.1533 z Diagonals of parallelogram bisect each other
4.183 z
31.6z