1. Warm Up 𝑚∠𝐴𝐵𝐶= 𝟖𝟐 𝒐 2.) 𝑚∠𝐴𝐵𝐷= 135 𝑜 . Solve for the 𝑚∠𝐴𝐵𝐶.
1.) Points A,B, and C are collinear. Point B is between A and C. Solve for x and justify each step. 𝐴𝐵=2𝑥+4, 𝐵𝐶=28, and 𝐴𝐶=6𝑥.
2.)
𝑚∠𝐴𝐵𝐷= 135 𝑜 . Solve for the 𝑚∠𝐴𝐵𝐶.
𝑚∠𝐴𝐵𝐶+𝑚∠𝐶𝐵𝐷=𝑚∠𝐴𝐵𝐷
4𝑥+2 + 3𝑥−7 =135
7𝑥−5=135
7𝑥=140
𝑥=20
𝑚∠𝐴𝐵𝐶=4𝑥+2
𝑚∠𝐴𝐵𝐶=
𝑚∠𝐴𝐵𝐶=80+2
𝑚∠𝐴𝐵𝐶= 𝟖𝟐 𝒐
Statements
Reasons
1.) 𝐴𝐵=2𝑥+4, 𝐵𝐶=28, and 𝐴𝐶=6𝑥.
1.) Given
2.) 𝐴𝐵+𝐵𝐶=𝐴𝐶
2.) Segment Addition Postulate
3.) 2𝑥 =(6𝑥)
3.) Substitution POE
4.) 2𝑥+32=6𝑥
4.) Simplify
5.) 32=4𝑥
5.) Subtraction POE
6.) 4𝑥=32
6.) Symmetric POE
7.) 𝑥=8
7.) Division POE

2. Angles and Parallel Lines
Mr. Riddle

3. Parallel Lines
When looking at a diagram, parallel lines are shown by arrowheads.
Line m is parallel to line p. m p

4. Transversals
A transversal is a line that intersects two or more coplanar lines at different points. t

5. Corresponding Angles
Corresponding Angles – in the diagram, and are corresponding angles. 2 6 t

6. Alternate Interior Angles
Alternate Interior Angles – and in the diagram, and are alternate interior angles. Opposite sides of the transversal and on the inside of the two lines. t 5 4

7. Alternate Exterior Angles
Alternate Exterior Angles – and in the diagram, and are alternate exterior angles. Opposite sides of the transversal and on the outside of the two lines. t 8 1

8. Same-Side Interior Angles
Same-Side Interior Angles and in the diagram and are consecutive interior angles. They lie between the two lines and on the same side of the transversal. t 7 3

9. Examples
Using the Diagram to the right. Describe the relationships between the angles.
1.)
2.)
3.)
4.)
5.)
6.)
Corresponding
Consecutive Interior
Alternate Exterior
Vertical
Alternate Interior
Linear Pair

10. Activity
1.) Draw two parallel lines on the graph of your whiteboard. 2.) Draw a transversal that goes through your parallel lines. 3.) Number your angles 1-8 from top right to bottom left. 4.) Measure all 8 of your angles and record their measures.

11. Activity
Based off of the angle measures you got, answer the following questions. Come up with a conclusion for each type of angle relationship. 5.) Corresponding Angles: 6.) Alternate Interior Angles: 7.) Consecutive Interior Angles: 8.) Alternate Exterior Angles:

12. Corresponding Angles
Corresponding Angles Postulate – If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent.
In the diagram, t 1 2

13. Alternate Interior Angles
Alternate Interior Angles Theorem – If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
In the diagram, t 4 3

14. Alternate Exterior Angles
Alternate Exterior Angles Theorem – If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
In the diagram, t 6 5

15. Consecutive Interior Angles
Consecutive Interior Angles Theorem - If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
In the diagram, ∠7 and ∠8 are supplementary. t 8 7

16. Example A: Using Algebra

18. ANSWERS: 3a: 𝒙=𝟐𝟎
3b: 𝒚=𝟑𝟖

19. Homework
ALEKS #10