1. HONORS GEOMETRY 4.1. Classifying Triangles

2. Do Now: No need to write things- just discuss with someone near you. What is a triangle? How many sides does a triangle have? How many angles does a triangle have?

3. Triangles For the next unit we will be talking about TRIANGLES And to classify triangles we can talk about either their ANGLES or their SIDES

4. Realize: When classifying triangles by angles…. Two angles in a triangle are always acute-- - therefore, we use the third one to classify the triangles by angles!

5. Types of Triangles (angles) 1. Acute Triangle 2. Equiangular Triangle 3. Obtuse Triangle 4. Right Triangle

6. Acute Triangle

7. Has 3 acute angles

8. Equiangular Triangle

9. Has three congruent angles! Pause…. What are the angles equal to??? Which means what other type of triangle do we have?

10. Obtuse Triangle

11. One Obtuse Angle

12. Right Triangle

13. One Right Angle

14. Example One:

15. Example Two: Classify the following triangles as acute, equiangular, obtuse, or right. Explain your reasoning. △ PQR △ QSR △ PQS

16. You Try! Classify △ XYZ as acute, equiangular, obtuse, or right. Explain your reasoning. What about △ XWY? △ WYZ?

17. Classifying Triangles by Sides 1. Equilateral Triangle 2. Isosceles Triangle 3. Scalene Triangle

18. Equilateral Triangle

19. Three Congruent Sides

20. Isosceles Triangle

21. Two congruent sides PAUSE: This means what else can we call an equilateral triangle?

22. Scalene Triangle

23. No congruent sides

24. Example Three:

25. Example Four:

26. You Try!

27. Realize….

28. Example Five: Find the measures of the sides of isosceles triangle △ ABC

29. You Try!

30. Triangle Angle Sum Theorem The sum of the measures of the angles in a triangle is 180 degrees.

31. How do we know!?!?!?

32. Example Six: Find x, y, and z

33. Example Seven: Find each of the number angles

34. You Try! Find the measure of each numbered angle.

35. Practice Problems Try some on your own/in small groups! As always if you are confused/have questions don’t hesitate to call me over!

36. Exit Ticket: Find x and then classify the triangle based on the angles.