1. Lesson 6 Parallel and Perpendicular lines

2. There exist different types of lines that will be explored in Geometry.
Parallel Lines are coplanar lines (lines that lie on the same plane) that do not intersect. The symbol ____ means “is parallel to.” ll
Arrows/triangles indicate that the lines above are parallel
So, p ll q

3. Perpendicular Lines are two lines that intersect to form right angles
Perpendicular Lines are two lines that intersect to form right angles. The symbol ___ means “is perpendicular to.” 
Two lines are perpendicular lines if they intersect to form 4 right angles. Lines t and u are perpendicular lines.
So, t  u

4. Skew Lines are two non-coplanar lines; skew lines are not parallel and do not intersect.
Not on the same plane
Not parallel
Not perpendicular
Do not intersect
Line m lies on plane A.
Line l passes through plane A.
So, line m and line l are skew.

5. Ex. 1 Determine whether the lines are parallel, perpendicular, or neither.
a. line v and line x
b. line v and line y
c. line w and line x
neither
parallel
perpendicular

6. Ex. 2 Determine whether the lines are skew. Explain your reasoning. a
Ex. 2 Determine whether the lines are skew. Explain your reasoning. a. line k and line m b. line l and line m
They are not skew because the lines intersect.
They are not skew because the lines are on the same plane (coplanar).

7. Theorems about Perpendicular Lines
There exists four theorems about perpendicular lines. Theorem 1: All right angles are congruent. Theorem 2: If two lines are perpendicular, then they intersect to form four right angles.
1 = 90o
2 = 90o
3 = 90o
4 = 90o
*Even if only one angle is marked as a right angle, the other 3 are automatically right angles.*

8. Ex. 4 In the diagram, HJ HL and mLHK = 42o. Find the value of z.

9. Open your textbooks P 110 #2-5, #10-14 (even) P 111 #15-19 (odd)

10. A transversal is a line that intersects two or more lines, each at a different point. When a transversal intersects two or more lines at different points, it forms eight angles. t 2 p 1 4 3 m 5 6 7 8
transversal

11. Two angles are corresponding angles if they have matching positions
Two angles are corresponding angles if they have matching positions. Corresponding angles also lie on the same side of a transversal. t r 1 2 4
To find the corresponding angles , draw a “F” using the transversal. 3 s 5 6 7 8
Corresponding Angles:
1 and 5
3 and 7
2 and 6
4 and 8

12. Corresponding Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are CONGRUENT. r
120◦ s
120◦

13. Two angles are alternate interior angles of they lie on opposite sides and at opposite ends of a transversal. t r 1 2 4
To find the alternate interior angles , draw a “Z” using the transversal.
Alternate interior means “in between” the lines. 3 s 5 6 7 8
Alternate Interior Angles:
3 and 6
4 and 5

14. Unit 2 - Parallel and Perpendicular Lines
Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are CONGRUENT r
70◦ s
70◦

15. Two angles are alternate exterior angles of they lie on opposite sides and at opposite ends of a transversal. t
To find the alternate exterior angles , draw a “Z” using the transversal.
Alternate exterior means “outside” the lines. r 1 2 4 3 s 5 6 7 8
Alternate Exterior Angles:
1 and 8
2 and 7

16. Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are CONGRUENT. r
130◦ s
130◦

17. Two angles are same-side interior angles if they lie between the two lines on the same side of the transversal. t
To find the same – side interior angles , draw a “C” using the transversal. r 1 2 4 3 s 5 6 7 8
Same Side Interior Angles:
3 and 5
4 and 6

18. Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of same – side interior angles are SUPPLEMENTARY r
70◦ s
110◦

19. Ex. 1 Identify the relationship between the angles.
a) 1 and 2
same – side interior angles
b) 4 and 6
corresponding angles
c) 3 and 6
alternate exterior angles 6 1 5 4 2 3

20. Ex. 2 List all the pairs of angles that fit the description.
a) Corresponding b) Alternate Interior
c) Alternate Exterior d) Same – Side Interior 8 1 4 2 7 3 5 6

21. Class Work
Pg 123 #2-14 (even) Pg 124 #16,18 Pg 125 # , , Pg. 132 #16-18 Pg. 133 #20, 26-28, 32– 34 (even) Pg. 134 36