1. 3.1 Lines and Angles
3.1 Lines and Angles

2. Objective: To Identify relationships between figures in a square
To identify angles formed by two lines and a transversal.
3.1 Lines and Angles

3. Vocabulary:
3.1 Lines and Angles

4. Vocabulary
Transversal – a line that intersects two coplanar lines at two distinct points.
3.1 Lines and Angles

5. Vocabulary <3, <4, <5, <6
Interior angles – Angles that are in between the two lines cut by a transversal
<3, <4, <5, <6
3.1 Lines and Angles

6. Vocabulary <1, <2, <7, <8
Exterior angles – Angles that are outside the two lines cut by a transversal
<1, <2, <7, <8
3.1 Lines and Angles
3.1 Lines and Angles

7. Vocabulary < 3 and < 6 < 4 and < 5
Alternate interior angles
< 3 and < 6
< 4 and < 5
3.1 Lines and Angles

8. Vocabulary < 2 and < 7 < 1 and < 8
Alternate exterior angles
< 2 and < 7
< 1 and < 8
3.1 Lines and Angles

9. Vocabulary < 1 and < 5 < 2 and < 6 < 3 and < 7
Corresponding Angles – angles that can “over-lap”
< 1 and < 5
< 2 and < 6
< 3 and < 7
< 4 and < 8
3.1 Lines and Angles

10. Vocabulary < 4 and < 5 < 3 and < 6
Same Side Interior Angles
< 4 and < 5
< 3 and < 6
3.1 Lines and Angles

11. Vocabulary < 1 and < 8 < 2 and < 7
Same Side Exterior Angles
< 1 and < 8
< 2 and < 7
3.1 Lines and Angles

12. Corresponding Angles Postulate
If a transversal intersects two parallel lines, then corresponding angles are congruent
m< 1 = m< 2
3.1 Lines and Angles

13. Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior angles are congruent
m< 5 = m< 6
m< 7 = m< 8
3.1 Lines and Angles

14. Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines, then same side interior angles are supplementary
= 1800
3.1 Lines and Angles

15. Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then alternate exterior angles are congruent
m< 1 = m< 2
m< 3 = m< 4
3.1 Lines and Angles

16. Same-side Exterior Angles Theorem
If a transversal intersects two parallel lines, then same side exterior angles are supplementary
3.1 Lines and Angles

17. Angle Relations:
3.1 Lines and Angles

18. Angle Relations:
3.1 Lines and Angles

19. Examples – interwrite activity
Random problems with different theorems
3.1 Lines and Angles

20. Parallelogram Problem
3.1 Lines and Angles

21. Parallelogram Problem
7x – 5 + (115) = 180
7x = 180
7x = 70
x = 10
5y = 180
5y = 65
y = 13
3.1 Lines and Angles

22. Lesson Check
3.1 Lines and Angles

23. Lesson Check
3.1 Lines and Angles