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Classifying Triangles Unit 4C-Triangle Geometry LT1: I can classify triangles based on angle measures. LT2: I can classify triangles based on side measures. Two Ways to Classify Triangles By Their Sides By Their Angles 2 Classifying Triangles By Their Sides Scalene Isosceles Equilateral 3 Scalene Triangles No sides are the same length 4 Isosceles Triangles At least two sides are the same length 5 Equilateral Triangles All three sides are the same length 6 Classifying Triangles By Their Angles Acute Right Obtuse 7 Acute Triangles Acute triangles have three acute angles 8 Right Triangles Right triangles have one right angle 9 Obtuse Triangles Obtuse triangles have one obtuse angle 10 Classify this triangle. Right Scalene 11 Classify this triangle. Obtuse Isosceles 12 Classify this triangle. Acute Scalene 13 Classify this triangle. Acute Isosceles 14 Classify this triangle. Obtuse Scalene 15 Classify this triangle. Right Isosceles 16 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. 17 Answer Time 1. Acute 10. Acute Isosceles 2. Right 11. Right Scalene 3. Obtuse 12. Obtuse Isosceles 4. 5. 6. 7. 8. 9. 13. Acute Equilateral 14. Obtuse Scalene 15. Right Scalene 16. Acute Isosceles 17. Obtuse Scalene 18. Acute Equilateral Acute Obtuse Acute Right Obtuse Acute 18 Any Questions???? 19 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. 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!!! 21 Angle Measures 60° + 60° + 60° = 180° 40° + 30° + 110° = 180° 22 Examples Will the following angle measures form a triangle? 1.) 80°, 40°, 60° 23 YES!!!!!!!!!!!! 80° + 40° + 60° = 180° 24 Examples 2.) 26°, 95°, 60° 25 NO!!!!!!!!!!!! 26° + 95° + 60° = 181° Remember, the sum of all three angles MUST equal 180°! 26 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! 27 Triangle Inequality Theorem Examples Will the following side lengths form a triangle? 1.) 10 in, 12 in, 14 in 29 YES!!!!!!!!!!!! 10 + 12 > 14 10 + 14 > 12 12 + 14 > 10 30 Examples 2.) 2 cm, 8 cm, 16 cm 31 NO!!!!!!!!!!!!!!!!!! 2 + 8 < 16 2 + 16 > 8 8 + 16 > 2 Remember, ALL statements MUST BE TRUE for a triangle to be made! 32 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. 33 Answer Time 1. Yes 7. Yes 2. No 8. Yes 3. No 9. No 4. Yes 5. Yes 6. Yes 10. No 11. Yes 12. Yes 34 Any Questions???? 35