MCC8.G.5

Angles and Parallel Lines

Intersecting Lines

• Lines that cross at exactly one point.

Perpendicular Lines

• Lines that intersect to form right angles.

PARALLEL LINES

• Def: line that do not intersect.

• Illustration:

• Notation: l || m AB || CD

lm

A

B

C

D

Examples of Parallel Lines

• Hardwood Floor

• Opposite sides of windows, desks, etc.

• Parking slots in parking lot

• Parallel Parking

• Streets

Examples of Parallel Lines

• Streets: Belmont & School

Transversal

• Definition: A line that intersects two or more lines in a plane at different points is called a transversal.

tm

n

Vertical Angles & Linear Pair

Vertical Angles:

Linear Pair:

1 4, 2 3, 5 8, 6 7

Two angles that are opposite angles. Vertical angles are congruent.

1 & 2 , 2 & 4 , 4 &3, 3 & 1,

5 & 6, 6 & 8, 8 & 7, 7 & 5

Supplementary angles that form a line (sum = 180)

1 23 4

5 6

7 8

Supplementary Angles/Linear Pair

• Two angles that form a line (sum=180)

1 2

3 4

5 6

7 8

t

5+6=1806+8=1808+7=1807+5=180

1+2=1802+4=1804+3=1803+1=180

Supplementary Angles/Linear Pair

• Find the measures of the missing angles

? 72

?

t

108

108 180 - 72

Complementary Angles

• Two angles whose measures add to 90˚.

Adjacent Angles

• Angles in the same plane that have a common vertex and a common side.

Angles and Parallel Lines

• If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.

1. Corresponding angles

2. Alternate interior angles

3. Alternate exterior angles

• If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.

1. Consecutive interior angles

2. Consecutive exterior angles Continued…..

Corresponding Angles

Corresponding Angles: Two angles that occupy corresponding positions.

2 6, 1 5, 3 7, 4 8

1 2

3 4

5 6

7 8

Consecutive Angles

Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.

Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal.

m3 +m5 = 180º, m4 +m6 = 180º

m1 +m7 = 180º, m2 +m8 = 180º

1 23 4

5 6

7 8

Alternate Angles

• Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair).

• Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.

3 6, 4 5

2 7, 1 8

1 2

3 4

5 6

7 8

Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles

when m< 1 = 100°. Justify your answers.

m<2=80° m<3=100° m<4=80°

m<5=100° m<6=80° m<7=100° m<8=80°

m<9=100° m<10=80° m<11=100° m<12=80°

m<13=100° m<14=80° m<15=100° m<16=80°

t

16 15

1413

12 11

109

8 7

65

34

21

s

DC

BA

Example:

1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.

If line AB is parallel to line CD and s is parallel to t, find:

2. the value of x, if m<1 = 100 and m<8 = 2x + 10.

3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.

ANSWERS:

t

16 151413

12 11

109

8 7

65

34

21

s

DC

BA

1. 30

2. 35

3. 33