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

It’s YOUR Turn! Now it’s your turn to practice classifying triangles. Complete BOTH sides of the worksheet On Side 1 (tic marks on the triangles) classify the triangles based on BOTH sides and angles. For example, an acute isosceles On Side 2 (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 Acute Isosceles 2. Right Scalene 3. Obtuse Isosceles 4. Acute Equilateral 5. Obtuse Scalene 6. Right Scalene 7. Acute Isosceles 8. Obtuse Scalene 9. Acute Equilateral 10. Acute 11. Right 12. Obtuse 13. Right 14. Obtuse 15. Acute 16. Acute 17. Obtuse 18. Acute

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 22 60° + 60° + 60° = 180°40° + 30° + 110° = 180°

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 30

Examples 2.) 2 cm, 8 cm, 16 cm 31

NO!!!!!!!!!!!!!!!!!! < > > 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 BOTH sides of the worksheet On Side 1 (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 Side 2 (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 Yes 2. No 3. No 4. Yes 5. Yes 6. Yes 7. Yes 8. Yes 9. No 10. No 11. Yes 12. Yes

Any Questions???? 35