1. Entry Task
3. Draw a large scalene triangle on the sheet of yellow copy paper. Then cut it out. We will be using the triangles for our lesson today.

2. Parallel Lines & Triangles
Lesson 3-5

3. Learning Targets I will be able to:
Find measures of angles in a given triangle;
Use parallel lines to prove a theorem about triangles;
Define and identify exterior angles of a triangle.

4. Investigation
Draw and cut out a large triangle. Without using a protractor to measure the angles, what is the sum of the angles measures of the triangle? Explain.
Tear off (don’t cut) the 3 angles of your triangle and rearrange them so that their vertices meet at a point. The sides should be adjacent and not overlapping. You may want to number the angles before you tear them off.
How does this arrangement show the sum of the angle measures?

5. Triangle Angle-Sum Theorem
The sum of the measures of the angles in a triangle is __________.
180⁰

6. How many lines can you draw through P parallel to line l ?

7. Parallel Postulate
Through a point not on a line, there is one and only one line parallel to the given line. P l

8. So what?
We can use the Parallel Postulate to prove the Triangle Angle-Sum Theorem 2 1 3

9. Example: Find the values of x, y, and z in the figure below.

10. What is an exterior angles of a triangle?
What are exterior angles?
remote interior angles
exterior angle

11. Triangle Exterior Angle Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

12. Examples:
2. What is the measure of ∠1? 3. What is the measure of ∠2? 4. The ratio of the angle measures of the acute angles in a right triangle is 2:3. Find the measures of the acute angles.

13. Homework
Page 175 (9-25 all, odds ) Mid-Unit Quiz tomorrow First four lessons only