Parallel Lines Properties of Angles Formed by Parallel Lines and a Transversal.
Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle...
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Transcript of Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle...
![Page 1: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/1.jpg)
Properties of Parallel Lines
Learning Target: I can use properties of parallel lines to find angle measures.
![Page 2: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/2.jpg)
A transversal is a line that intersects two coplanar lines at two different points.
When a transversal intersects those two lines it creates eight angles.
1 23 4
5 67 8
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·Inside the two parallel lines ·Opposite sides of the transversal
·Examples 3 & 6 4 & 5
Alternate Interior Angles
1 2
3 4
5 6
7 8
Alternate Interior Angles are always congruent!
![Page 4: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/4.jpg)
·Inside the parallel lines
·On the same side of the transversal
Examples: 3 & 5 4 & 6
Same-Side Interior Angles
1 23 4
5 6
7 8
Same-Side Interior Angles are always supplementary (add to 1800)
![Page 5: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/5.jpg)
Corresponding Angles
Lie on the same side of the transversal in corresponding positions
Examples: 1 & 5 2 & 6 3 & 7 4 & 8
1 2
3 4
5 6
78
Corresponding Angles are always congruent.
![Page 6: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/6.jpg)
12
34
5 6
7 8
Alternate exterior angles·lie on opposite sides of the transversal
·nonadjacent exterior angles
![Page 7: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/7.jpg)
Examples:
Find m<1 and m<2
750
1
2
t
n
m
1=750
2=1050
![Page 8: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/8.jpg)
Examples:
Find m<1 and m<2.
1200
a b
21
q
1=1202=60
![Page 9: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/9.jpg)
Try this with your partner:
Find m<3 m<4 m<5m<6 m<7 m<8
a
b
cd
8 7 62500
51 3
4
3=1304=1305=506=507=1308=50
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800 700
1 2
Find m<1 and m<2.
2=701=100
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(x+40)0
x0
Find the value of the measured angles.
x+40+x=1802x+40=1802x=140x=70
![Page 12: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/12.jpg)
Find the value of the labeled angles.
(x+40) 0
(3x-10) 0
3x-10=x+402x=50x=25
![Page 13: Properties of Parallel Lines Learning Target: I can use properties of parallel lines to find angle measures.](https://reader035.fdocuments.us/reader035/viewer/2022062412/5a4d1b027f8b9ab059986e7e/html5/thumbnails/13.jpg)
x0 y0
500
700
Find x and y.
x=70x+y+50=18070+y+50=180120+y=180y=60