1. 4-3 Angle Relationship in triangles
Chapter 4
4-3 Angle Relationship in triangles

2. SAT Problem of the day

3. solution
Right Answer: A

4. Objectives
Find the measures of interior and exterior angles of triangles.
Apply theorems about the interior and exterior angles of triangles.

5. sum of the interior angles of a triangle
Do you know what is an interior angle of a triangle?
Answer: They are the angles in the inside of a triangle
Do you know what is an exterior angle of a triangle?
Answer: they are the angles form in the outside of a triangle
Who much do all the interior angles of a triangle add up?
Answer: they add up to 180 degrees

6. What is an auxiliary line?
An auxiliary line is a line that is added to a figure to aid in a proof.

7. Example#1
Use the diagram drawn below to find mXYZ

8. Example#2
Use the diagram drawn below to find mYWZ.

9. Example#3
Use the diagram to find mMJK.

10. Student guided practice
DO problems in the worksheet and 4 and 5 in your book page 235

11. What is a corollary?
A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

12. Example#4
One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

13. Example#5
The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

14. Student guided practice
Do problems 6 to 8 in your book page 235

15. Angle relationship
The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure.
Exterior
Interior

16. Angle relationship
An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side.
Interior angle <3 and exterior angle <4

17. Angle relationship
Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle.
The remote interior angles of 4 are 1 and 2.

18. Exterior angle theorem

19. Example#6
Find mB.

20. Example#7
Find mACD.

21. Student guided practice
Do problems 9 and 10 in your book page 235

22. Third angle theorem

23. Example#8
Find mK and mJ

24. Example#9
Find mP and mT.

25. Student Guided practice
Do problems 12 and 13 in your book page 235

26. Homework!!!
Do problems in your book page 236

27. Closure Today we learned about angles of triangles
Next class we are going to learn about congruent triangles