1. Properties of Parallel Lines
Tutorial 7c

2. Angles and Intersecting Lines
A transversal is a line that intersects two coplanar lines at two distinct points.
Line t below is a transversal because it intersects lines l and m 1 2 l
1, 2, 7, and 8 are all considered to be exterior angles. 3 4
3, 4, 5, and 6 are all considered to be interior angles. 5 6 m 7 8 t

3. Angles and Intersecting Lines
Corresponding Angles:
A pair of angles that lie on the same side of the transversal yet one lies on the interior and one lies on the exterior.
1 and 5
2 and 6
3 and 7
4 and 8
Alternate Interior angles:
A pair of interior angles that lie on alternate sides of the transversal.
3 and 6
4 and 5
Same-side Interior angles:
A pair of interior angles that lie on the same side of the transversal.
3 and 5
4 and 6 1 2 l 3 4
Alternate-Exterior angles:
A pair of exterior angles that lie on the alternate sides of the transversal.
1 and 8
2 and 7 5 6 m 7 8 t

4. Parallel Lines
Parallel Lines are two or more lines on the same plane(coplaner) that do not intersect. m n
m || n
Line m is parallel to line n.
We can write this using the following symbol

5. Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Corresponding Angles
1  5
2  6
3  7
4  8 l 1 2 4 3 5 6 m 7 8 t

6. Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
Alternate Interior angles
3  6
4  5 l 1 2 4 3 5 6 m 7 8

7. Same-Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. l 1 2 4 3 5 6 m 7 8

8. Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
Alternate Exterior angles
1  8
2  7 l 1 2 4 3 5 6 m 7 8

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10. Corresponding Angles
Alternate Interior Angles
Same-side Interior Angles
4. Alternate Interior Angles
Same-side Interior Angles
Corresponding Angles

11. *Double arrows mean that the lines are parallel.
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12. *Double arrows mean that the lines are parallel.
Same-side Interior Angles
x = 180
x = 59
Same-side Interior Angles
x = 180
x = 63
Same-side Interior Angles
x + 74 = 180
x = 106
Same-side Interior Angles
x + 68 = 180
x = 112
Same-side Interior Angles
x = 180
x = 71
Same-side Interior Angles
x + 90 = 180
x = 90

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14. m1 = 60º Alternate Interior Angles:
Alternate Interior Angles: m1 = 130º
Alternate Interior Angles: m1 = 40º

15. The End
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