1. Geometry 3.1
Brett Solberg AHS ’11-’12

2. Warm-up Use the vertical angles theorem to solve for x.
Pick up a green notes packet for chapter 3 from the back table.

3. Real Salt Lake 11 players Goalkeeper GK Defender D Midfielder M
Forward F

5. Geometric Application
Angles in certain positions have special properties.
Transversal: a line that intersects two lines.
A transversal creates 8 angles.
1 2
4 3
8 7

6. Interior Angles Interior 1 2 4 3 5 6 8 7
1 2
4 3
8 7
Interior
∠3, ∠4, ∠5, ∠6 are interior angles.

7. Exterior Angles
∠1, ∠2, ∠7, and ∠8 are exterior angles

8. Alternate Interior Angles
1 2
4 3
8 7
∠3 and ∠5 are alternate interior angles.
∠4 and ∠6 are alternate interior angles.

9. Corresponding angles
1 2
4 3
∠1 and ∠5 are corresponding angles.
∠2 and ∠6 are corresponding angles.
∠3 and ∠7 are corresponding angles.
∠4 and ∠8 are corresponding angles.

10. Same-side Interior Angles
1 2
4 3
∠3 and ∠6 are same-side interior angles.
∠4 and ∠5 are same-side interior angles.

11. Alternate Exterior Angles
∠1 and ∠7 are alternate exterior angles.
∠2 and ∠8 are alternate exterior angles.

12. Postulate 3-1
If a transversal intersect two parallel lines, then corresponding angles are congruent. 1 2
∠1 ≅ ∠2

13. Theorem 3-1
If a transversal intersect two parallel lines, then alternate interior angles are congruent. 1 2
∠1 ≅ ∠2

14. Theorem 3-2
If a transversal intersect two parallel lines, then same-side interior angles are supplementary. 1 2
∠1 + ∠2 = 180

15. Theorem 3-3
If a transversal intersect two parallel lines, then alternate exterior angles are congruent. 1 2
∠1 ≅ ∠2

16. Theorem 3-4
If a transversal intersect two parallel lines, then same-side exterior angles are supplementary. 1 2
∠1 + ∠2 = 180

17. Example 3
Find the m∠1 and m ∠2. Justify your answer. 42 2 1

18. Example 4
Find a, b, c. Justify your answers. a c b 40 65

19. Find x, y, and the measure of all angles.

20. Homework
3.1 Worksheet