Properties of Parallel Lines

Learning Target: I can use properties of parallel lines to find angle measures.

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

·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!

·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)

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.

12

34

5 6

7 8

Alternate exterior angles·lie on opposite sides of the transversal

·nonadjacent exterior angles

Examples:

Find m<1 and m<2

750

1

2

t

n

m

1=750

2=1050

Examples:

Find m<1 and m<2.

1200

a b

21

q

1=1202=60

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

800 700

1 2

Find m<1 and m<2.

2=701=100

(x+40)0

x0

Find the value of the measured angles.

x+40+x=1802x+40=1802x=140x=70

Find the value of the labeled angles.

(x+40) 0

(3x-10) 0

3x-10=x+402x=50x=25

x0 y0

500

700

Find x and y.

x=70x+y+50=18070+y+50=180120+y=180y=60