1. Angles and Parallel Lines
Geometry Review
Angles and Parallel Lines
Objectives: Measure and Classify Angles Describe Angle Pair Relationships Classify Angle Pairs made by Parallel Lines cut by a Transversal Describe Angle Pair Relationships within Parallel Lines

2. Part 1: Angles
An angle consists of two different rays (sides) that share a common endpoint (vertex).
Vertex
Sides
This angle can be called: Angle ABC, <ABC, <CBA
OR it can be named by the vertex like so: <B

3. Types of Angles
Go to the following website to learn about the different types of angles.
Don’t forget to press the play button on top of the picture to see the animation.
Use the diagram to find the measure of the indicated angle. Then classify each angle as either acute, right, obtuse, or straight.
KHJ
GHK
GHJ
GHL

4. 5.
What is the measure of DOZ?... How did you get to your answer?

5. Angle Addition Postulate
If P is in the interior of RST, then mRST = mRSP + mPST.

6. 6.
Given that mLKN = 151°, find mLKM and mMKN.

7. Congruent Angles
Two angles are congruent angles if they have the same measure.

8. Angle Bisector
An angle bisector is a ray that divides an angle into two congruent angles.

9. 7.
Ray BD bisects <ABC. Solve for x. A D B C

10. 8.
In a diagram, YW bisects XYZ. mXYW = ° and m ZYW= (-18m)°. Find mXYW.
Hint: Draw the picture
Hint: Angle may not be drawn to scale

11. C Comes Before S… Complementary Angles Sum to 90 Degrees Supplementary Angles Sum to 180

12. Linear Pairs of Angles

13. Linear Pairs of Angles
Two adjacent angles form a linear pair if their noncommon sides are opposite rays.
The angles in a linear pair are supplementary.

14. Vertical Angles

15. Vertical Angles
Two nonadjacent angles are vertical angles if their sides form two pairs of opposite rays.
Vertical angles are formed by two intersecting lines.

16. Name a pair of complementary angles.
Name a pair of supplementary angles.
Name a linear pair.
Name a pair of vertical angles.
Name a pair of congruent angles. U Y T V X W

17. Part 2: Parallel Lines
What would you call two lines which do not intersect?
Answer: Parallel Lines
A solid arrow placed on two lines of a diagram indicate the lines are parallel.
Exterior
Interior
The symbol || is used to indicate parallel lines.
Exterior
AB || CD

18. A slash through the parallel symbol || indicates the lines are not parallel.
AB || CD

19. Transversal
Definition: A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments.
transversal
Exterior
Exterior
transversal
Parallel lines
Non-Parallel lines
Interior
Interior
Exterior
Exterior

20. Transversal -
A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel.
Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

21. 1 2 3 4 5 6 7 8 INTERIOR –The space INSIDE the 2 lines
In the diagram below:
Angles 1, 2, 7 and 8 are exterior angles.
Angles 3, 4, 5, and 6 are on the interior.
EXTERIOR The space OUTSIDE the 2 lines
exterior
Exterior 1 2 3 4
Interior 5 6 7 8
Exterior

22. When two parallel lines are cut by a transversal special angle relationships form.
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are CONGRUENT
♥Same Side Interior Angles are SUPPLEMENTARY
♥Same Side Exterior Angles are SUPPLEMENTARY 1 4 2 6 5 7 8 3
Exterior
Interior
Exterior

23. Corresponding Angles
Corresponding Angles: Two angles that occupy corresponding positions.
 2   6,  1   5,  3   7,  4   8
Exterior 1 2 3 4
Interior 5 6 7 8
Exterior

24. Corresponding Angles ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF
When two parallel lines are cut by a transversal, pairs of corresponding angles are formed.
Line M B A
Line N D E L P Q G F
Line L
ÐGPB = ÐPQE
ÐGPA = ÐPQD
ÐBPQ = ÐEQF
ÐAPQ = ÐDQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.

25. Lines l and m are parallel. l||m.
14. Name all pairs of corresponding angles.
15. Determine all the missing angle measures.
42°
a ° c° b° l d° e° g° f° m

26. Same Side Interior/Exterior Angles
Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.
Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal.
ÐAPQ + ÐDQP = 1800
ÐBPQ + ÐEQP = 1800
Line M B A
Line N D E L P Q G F
Line L
Exterior
600
1200
Same Side Interior or Same Side Exterior angles are supplementary.
Interior
600
1200
Exterior

27. Alternate Interior/Exterior 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.
Line M B A
Line N D E L P Q G F
Line L
ÐBPQ = ÐDQP
ÐAPQ = ÐEQP
Two pairs of alternate angles are formed.
Pairs of alternate angles are congruent.

28. 17. Name all pairs of alternate exterior angles.
Lines l and m are parallel. l||m 16. Name all pairs of alternate interior angles.
17. Name all pairs of alternate exterior angles.
18. Determine all the missing angle measures.
81°
a ° c° b° l d° e° g° f° m

29. Corresponding angles Alternate angles Interior angles Test Yourself
Make sure you are in slide show view to do this test. Name the pairs of the following angles formed by a transversal.
Line M B A
Line N D E P Q G F
Line L
Line M B A
Line N D E P Q G F
Line L
500
1300
Line M B A
Line N D E P Q G F
Line L
Test Yourself
Corresponding angles
Interior angles
Alternate angles

30. 19) Find the missing angles.
70 °
70 ° b°
Hint: The 3 angles in a triangle sum to 180°.
d °
65 °

31. 20) Find the missing angles.
45 °
50 ° b°
Hint: The 3 angles in a triangle sum to 180°.
d °
75 °

32. 21. Name the angles congruent to 3.
In the figure a || b.
21. Name the angles congruent to 3.
22. Name all the angles supplementary to 6.
23. If m1 = 105° what is m3?
24. If m5 = 120° what is m2?

33. 25. Final Exercise
40°
Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.
60°