Welcome Geometry!

1. Welcome Geometry! • Take out your homework • Take out your whiteboard and whiteboard pens. • Take out a piece of paper and title it: • 4.2: Angle Relationships in Triangles

2. Transformation Test • A: 28-31 • B: 25- 27.5 • C: 22-24.5

3. Test Corrections • This will count as a 5 point homework assignment due TOMORROW

4. Whiteboards: DO NOW Classify each triangle by its angles and sides. 1. MNQ 2.NQP MNP

5. Whiteboards • Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80° • What is the complement of an angle with measure 17°?

6. 4.2: Angle Relationships in Triangles • Learning Objective • SWBAT find the measures and apply theorems of interior and exterior angles of triangles.

7. MATH JOKE OF THE DAY • How many feet are in a yard? • It depends on how many people are in the yard!

8. Materials • Patty paper • Straightedge • Piece of paper split in half • Pencil/eraser

9. Directions • Draw and label triangle ABC on your paper • On patty paper, draw a line l and label a point P on the line • Place line l on AB and place point P on angle B of your triangle. Trace angle B.

10. Directions • Rotate the triangle until point P is on Angle C and trace angle C. It should be adjacent to Angle B. • Rotate the triangle again and trace angle A adjacent to angle C.

11. Answer the following Question on your Notes: • What do you notice about the three angles of the triangle?

12. Now do it Again… • With a different size triangle • What do you observe about your results?

13. Write an equation describing the relationship among the measures of the interior angles in a triangle. • This is the Triangle Sum Theorem • Tape your triangle and patty paper in your notebooks.

14. Triangle Sum Theorem

15. CY2 X 4 1 5 2 3 B A An auxiliary line is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem

16. C X 4 1 5 Talk with your group… 2 3 B A • What is the relationship between angles 1 and 4? • What is the relationship between angles 3 and 5? • Using the angle addition postulate, what do angles 1, 2 and 3 equal?

17. Proofs are Back!!!!

18. Example 1: Application Afteran accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find mXYZ. Find mYWZ mXYZ + mYZX+ mZXY= 180°

19. Whiteboards • Use the diagram to find mMJK.

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

21. Example 2: Finding Angle Measures in Right Triangles One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle? Let the acute angles be A and B, with mA = 2x°. mA + mB = 90° 2x+ mB = 90 mB = (90 – 2x)°

22. Whiteboards • The measure of one of the acute angles in a right triangle is x°. What is the measure of the other acute angle?

23. Interior • all points inside the figure • Exterior • all points outside the figure. • What are the interior angles? • What are the exterior angles? Exterior Interior

24. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its non-adjacent interior angles • 4= 1 + 2

25. Example 3: Applying the Exterior Angle Theorem Find mB.

26. Whiteboards Find mACD.

27. Third Angle Theorem

28. Example 4: Applying the Third Angle Theorem Find mK and mJ.

29. Whiteboards Find mPand mT.

30. Whiteboards 1. The measure of one of the acute angles in a right triangle is 56 °. What is the measure of the other acute angle? 2. Find mABD. 3. Find mNandmP. 124° 75°; 75°

31. WHITEBOARDS 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store?