1. Properties of Parallel Lines
Section 3-2
section 3-2

2. What we will cover… Corresponding Angles Alternate Interior Angles
Same-side Interior Angles
What we can prove.
section 3-2

3. Corresponding Angles
Corresponding angles lie in the same place with regard to the original lines and the transversal.
If we take an overhead picture of the two intersections, they will lie in the same part of the picture
section 3-2

4. Corresponding Angles on Parallel Lines
When the lines are parallel…
What do you think will be true of the corresponding angles here?
THEY ARE CONGRUENT
section 3-2

5. The Corresponding angles will stay congruent1 1 2 2
section 3-2

6. A Proof Given: lines k and l with corresponding angles 1 and 2
Prove: m<2 = m<3 1 k 3 2 l
section 3-2

7. Alternate Interior Angles
Alternate Interior angles lie between the parallel lines and on opposite sides of the transversal.
section 3-2

8. Alternate Interior Angles
When we look at the alternate interior angles on parallel lines…
What do you think about these angles?
THEY ARE CONGRUENT
section 3-2

9. Same-side Interior Angles
These will be between the parallel lines on the same side of the transversal
Lets take a look at the same-side interior angles…
Do they look congruent? NO
They are supplementary.
section 3-2

10. What This Means When we have parallel lines cut by a transversal:
Corresponding angles are congruent.
Alternate interior angles are congruent.
Same-side interior angles are supplementary
section 3-2

11. Example 1: What is the value of y if lines a and b are parallel?
What is the relationship between the angles?
Then they must be:
(y+50)° a
(2y)° b
Corresponding
(2y) = (y+50)
y = 50
Congruent
section 3-2

12. Example 2: What is the value of x if lines p and q are parallel?
What relationship do the angles have?
This means they are: q
(x+20)°
(x–10)° p
(x+20) + (x–10) = 180
2x + 10 = 180
x = 85
Same-side interior
Supplementary
section 3-2

13. What we can prove… Take a look at these angles…
What do you think will be true about these?
How about these angles?
They are congruent
They are congruent
**Some texts call these alternate exterior angles.
section 3-2

14. Theorem 3-4
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also 1
m<1 = 90˚
section 3-2

15. Are there parallel lines here?
section 3-2

16. Are these lines parallel? …or even straight?
section 3-2

17. Are these lines parallel?
section 3-2