Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

• Perpendicular lines are two lines that intersect to form a 90 degree angle

•

Parallel and Perpendicular Lines

• Parallel lines are two lines that, if extended forever, would never cross or touch

• In the figure below, line l is parallel to line m • (l // m )

l m

Parallel and Perpendicular Lines Checkpoint

• Name all sets of parallel line segments in each of the figures below:

a b e

f

d c h g

Lines AB and DC, AD and BC, and EH and FG

Parallel and Perpendicular Lines Checkpoint

• Name all sets of perpendicular line segments in each of the figures below:

a b e

f

d c h g

Lines AD and DC, DC and BC, AB and BC, AB and AD, EH and GH, and GH and FG

Transversals• A line that intersects two other lines is called a

transversal• In the figure below, l || m and n is the

transversal• Eight angles are formed when a transversal

intersects two parallel lines1 2

34

5 6

78

l

mn

Transversal Mini-Lab

For this mini-lab, you will need:

• Notebook paper

• Pencil

• Two colored pencils (share with neighbor)

• Ruler (share with neighbor)

• Protractor

Transversal Mini-Lab1. Draw two parallel lines using the lines on your

notebook paper.

2. Using a ruler, draw any line (not perpendicular) to intersect these two parallel lines.

3. Label the angles formed using the numbers 1 – 8 as shown below:

1 2

34

5 6

78

l

m

n

Transversal Mini-Lab

4. Use a protractor to measure each angle and record it’s measurement below your figure (example: m 2 = 28 degrees)

5. Shade angle 1 and each angle that has a congruent measurement with a colored pencil.

6. Shade angle 2 and each angle that has a congruent measurement with another colored pencil.

7. Compare your results with a neighbor and be prepared to discuss

Transversal Mini-Lab (what do you already know?)

• Angles 1 and 2 are supplementary angles and must equal 180 degrees

1 2

34

5 6

78

l

m

n

Transversal Mini-Lab (what do you already know?)

• Angles 1 and 3 and angles 2 and 4 are vertical angles that have the same measure.

1 2

34

5 6

78

l

m

n

Congruent Angles with Parallel Lines

• The symbol means congruent to

• If a pair of parallel lines is intersected by a transversal, pairs of congruent angles are formed

1 2

34

5 6

78

l

m

n

Congruent Angles with Parallel Lines

• Congruent angles formed in between the parallel lines are known as alternate interior angles

• 4 6 and 3 5

1 2

34

5 6

78

l

m

n

Congruent Angles with Parallel Lines

• Congruent angles formed outside of the parallel lines are known as alternate exterior angles

• 1 7 and 2 8

1 2

34

5 6

78

l

m

n

Congruent Angles with Parallel Lines

• Congruent angles formed in the same position on the two parallel lines in relation to the transversal are known as corresponding angles

• 1 5; 2 6; 3 7; and 4 8

1 2

34

5 6

78

l

m

n

Congruent Angles with Parallel Lines Checkpoint

• In the figure below, m 1 = 65• Explain how you find the measure of each of the

rest of the angles using vocabulary words such as supplementary, vertical, corresponding, alternate interior, and alternate exterior angles

1 2

34

5 6

78

l

m

n

Congruent Angles with Parallel Lines and Equations

• In the figure below, m 1 = 11x • m 6 = 5x + 100 • Find the value of x and then find the measure of

the remaining angles

1 2

34

5 6

78

l

mn

Hint: Angles 2 and 6 are Corresponding and angles 1 and 2 are Supplementary

Homework

• Skill 2: Parallel and Perpendicular Lines (both sides)

• Practice 6-1: Line and Angle Relationships (both sides)

• Due Tomorrow!