1. Parallel and Perpendicular Lines

2. Parallel and Perpendicular Lines
Perpendicular lines are two lines that intersect to form a 90º angle

3. Parallel and Perpendicular Lines
Parallel lines are two lines that, if extended indefinitely, would never cross or touch
In the figure below, line l is parallel to line m
l ll m
l m

4. Parallel and Perpendicular Lines Checkpoint
Name all pairs of parallel line segments in each of the figures below:
a b e f
d c h g
AB ll DC, AD ll BC, and EH ll FG

5. Parallel and Perpendicular Lines Checkpoint
Name all pairs of perpendicular line segments in each of the figures below:
a b e f
d c h g
AD DC, DC BC, AB BC, AB AD, EH GH, and GH FG

6. 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 lines 1 2 3 4 5 6 7 8 l m n

7. Transversal Mini-Lab For this mini-lab, you will need: Notebook paper
Pencil
Two colored pencils (share with neighbor)
Ruler (share with neighbor)
Protractor

8. Transversal Mini-Lab
Draw two parallel lines using the lines on your notebook paper.
Using a ruler, draw any line (not perpendicular) to intersect these two parallel lines.
Label the angles formed using the numbers 1 – 8 as shown below: 1 2 3 4 5 6 7 8 l m n

9. Transversal Mini-Lab
Use a protractor to measure each angle and record it’s measurement below the figure (example: m 2 = 28º)
Shade angle 1 and each angle that has a congruent measurement with a colored pencil.
Shade angle 2 and each angle that has a congruent measurement with another colored pencil.
Compare your results with a neighbor and be prepared to discuss

10. Transversal Mini-Lab (what do you already know?)
Angles 1 and 2 are supplementary angles and must equal 180º 1 2 3 4 5 6 7 8 l m n

11. 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 3 4 5 6 7 8 l m n

12. 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 3 4 5 6 7 8 l m n

13. Congruent Angles with Parallel Lines
Congruent angles formed in between the parallel lines are known as alternate interior angles
and 1 2 l 4 3 5 6 m 8 7 n

14. Congruent Angles with Parallel Lines
Congruent angles formed outside of the parallel lines are known as alternate exterior angles
and 1 2 l 4 3 5 6 m 8 7 n

15. 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
; ; ; and 1 2 l 4 3 5 6 m 8 7 n

16. 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 3 4 5 6 7 8 l m n

17. Congruent Angles with Parallel Lines Checkpoint
Measure
Concept 1
65°
Given 2
115°
Supplementary with 1 3
Vertical with 1 4
Vertical with 2 5
Corresponding with 1, Alt. Interior with 3 6
Corresponding with 2, Alt. Interior with 4 7
Corresponding with 3, Alt. Exterior with 1, Vertical with 5 8
Corresponding with 4, Alt. Exterior with 2, Vertical with 6 1 2 3 4 5 6 7 8 l m n

18. Congruent Angles with Parallel Lines and Equations
In the figure below, m 1 = 11x
m 6 = 5x
Find the value of x and then find the measure of the remaining angles
Hint: Angles 2 and 6 are Corresponding and angles 1 and 2 are Supplementary 1 2 4 3 l 5 6 8 7 m n

19. Congruent Angles with Parallel Lines and Equations
1 = 11x°, 6 = 5x° °
11x° + 5x° + 100° = 180°
16x° + 100° = 180°
16x° = 80°
x° = 5°
Angle
Measure
Concept 1
55°
Supplementary with 6, 11(5) = 55 2
125°
Corresponding with 6 3
Vertical with 1 4
Vertical with 2 5
Corresponding with 1, Alt. Interior with 3 6
Supplementary with 1, 5(5) = 125 7
Corresponding with 3, Alt. Exterior with 1, Vertical with 5 8
Corresponding with 4, Alt. Exterior with 2, Vertical with 6 1 2 3 4 5 6 7 8 l m n

20. Homework Skill 2: Parallel and Perpendicular Lines (both sides)
Practice 6-1: Line and Angle Relationships (both sides)
Due Tomorrow!