Classifying Triangles

1. Classifying Triangles Unit 4C-Triangle Geometry • LT1: I can classify triangles based on angle measures. • LT2: I can classify triangles based on side measures.

2. Two Ways to Classify Triangles • By Their Sides • By Their Angles

3. Classifying Triangles By Their Sides • Scalene • Isosceles • Equilateral

4. Scalene Triangles • No sides are the same length

5. Isosceles Triangles • At least two sides are the same length

6. Equilateral Triangles • All three sides are the same length

7. Classifying Triangles By Their Angles • Acute • Right • Obtuse

8. Acute Triangles • Acute triangles have three acute angles

9. Right Triangles • Right triangles have one right angle

10. Obtuse Triangles • Obtuse triangles have one obtuse angle

11. Classify this triangle. Right Scalene

12. Classify this triangle. Obtuse Isosceles

13. Classify this triangle. Acute Scalene

14. Classify this triangle. Acute Isosceles

15. Classify this triangle. Obtuse Scalene

16. Classify this triangle. Right Isosceles

17. It’s YOUR Turn! • Now it’s your turn to practice classifying triangles. • Complete Side 1 (LT1-2) of the worksheet • On the bottom half (tic marks on the triangles) classify the triangles based on BOTH sides and angles. For example, an acute isosceles • On the top half (no tic marks on the triangles) classify the triangles based only on angles. For example, acute. • You will have 10 minutes to complete this worksheet before we discuss your findings as a class.

18. Answer Time 1. Acute 10. Acute Isosceles 11. Right Scalene 2. Right 12. Obtuse Isosceles 3. Obtuse 13. Acute Equilateral 4. Acute 14. Obtuse Scalene 5. Obtuse 15. Right Scalene 6. Acute 7. Right 16. Acute Isosceles 17. Obtuse Scalene 8. Obtuse 18. Acute Equilateral 9. Acute

19. Any Questions????

20. Identifying Triangles Unit 4C-Triangle Geometry • LT3: I can identify whether given angle measures form a triangle. • LT4: I can identify whether given side lengths form a triangle.

21. Triangles Based On Angles • The sum of all angles in a triangle MUST equal 180˚!!!!!!!!!!!!!!! • What does “sum” mean? • How many angles does a triangle have? • If the sum of all angles in a triangle does NOT equal 180° a triangle cannot be formed!!!

22. Angle Measures 60° + 60° + 60° = 180° 40° + 30° + 110° = 180°

23. Examples • Will the following angle measures form a triangle? • 1.) 80°, 40°, 60°

24. YES!!!!!!!!!!!! • 80° + 40° + 60° = 180°

25. Examples • 2.) 26°, 95°, 60°

26. NO!!!!!!!!!!!! • 26° + 95° + 60° = 181° • Remember, the sum of all three angles MUST equal 180°!

27. Side Lengths • The Triangle Inequality Theorem states that any side of a triangle is always shorter than the sum of the other two sides. • A + B > C and A + C > B and B + C > A with A, B, and C being the three sides of the triangle. • If ANY of the above is NOT TRUE then a triangle cannot be formed!

28. Triangle Inequality Theorem

29. Examples • Will the following side lengths form a triangle? • 1.) 10 in, 12 in, 14 in

30. YES!!!!!!!!!!!! • 10 + 12 > 14 • 10 + 14 > 12 • 12 + 14 > 10

31. Examples • 2.) 2 cm, 8 cm, 16 cm

32. NO!!!!!!!!!!!!!!!!!! • 2 + 8 < 16 • 2 + 16 > 8 • 8 + 16 > 2 • Remember, ALL statements MUST BE TRUE for a triangle to be made!

33. It’s YOUR Turn! • Now it’s your turn to practice identifying triangles. • Complete Side 2 of the worksheet • On the top half (side measurements) determine if a triangle can be made or not by placing “Yes” or “No” in the first column. Then, in the second column, prove or disprove your answer using the Triangle Inequality Theorem. • On the bottom half (angle measures) determine if a triangle can be made or not by placing “Yes” or “No” in the first column. Then, in the second column, prove or disprove your answer. • You will have 20 minutes to complete this worksheet before we discuss your findings as a class.

34. Answer Time 1. Yes 7. Yes 8. Yes 2. No 9. No 3. No 10. No 4. Yes 11. Yes 5. Yes 12. Yes 6. Yes

35. Any Questions????