1. Q4W2: Angles and Transversals

2. Objectives I understand why an exterior angle of a triangle is equal to the sum of the opposite interior angles. I understand the angle relationships that occur when parallel lines are cut be a transversal.

3. Vocabulary Supplementary Angles: Two angles that add up to 180 degrees. Together they form a straight line.

4. What is the measure of the missing angle?

5. Triangle Review The angles of a triangle always add up to 180 degrees.

6. Angles When the sides of a triangle are extended, other angles are formed:

7. Angles Knowing that supplementary angles always add up to 180, what is the missing angle?

8. Find the missing EXTERIOR angle. Note: Not to scale

9. External Angle Theorem

10. Exterior Angle Theorem

11. Using the Exterior Angle Theorem

13. Parallel Lines & Transversals What is a transversal? A transversal is a line that crosses at least two other lines.

14. Parallel Lines & Transversals When two parallel lines are cut by a transversal, pairs of congruent and supplementary angles are formed. In geometry, “congruent” means “same.”

15. Parallel Lines & Transversals Congruent Angles There are 4 types of congruent angles that are created when parallel lines are crossed by a transversal. 1. Vertical Angles 2. Alternate Interior Angles 3. Alternate Exterior Angles 4. Corresponding Angles

16. Vocabulary Vertical Angles: each of the pairs of opposite angles formed when parallel lines are crossed by a transversal.

17. Vocabulary Corresponding Angles: the angles that occupy the same relative position when parallel lines are crossed by a transversal.

18. Congruent Angles When parallel lines are crossed by a transversal, alternate interior and alternate exterior angles are also congruent!

19. Parallel Lines & Transversals Name the Congruent Angles 1. Vertical Angles: _____________________________ 2. Alternate Interior Angles: ___________________ 3. Alternate Exterior Angles: ___________________ 4. Corresponding Angles: ______________________

20. Fill in the missing angle measurements Due to all of these congruent and supplementary angles, if you know one angle measurement, you can name them all!