classifying triangles unit 4c-triangle geometry lt1: i can classify triangles based on angle...
TRANSCRIPT
Classifying TrianglesClassifying Triangles
Unit 4C-Triangle Geometry
LT1: I can classify triangles based on angle measures.LT2: I can classify triangles based on side measures.
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Two Ways to Classify TrianglesTwo Ways to Classify Triangles
By Their SidesBy Their Angles
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Classifying Triangles Classifying Triangles By Their SidesBy Their Sides
Scalene IsoscelesEquilateral
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Scalene TrianglesScalene Triangles
No sides are the same length
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Isosceles TrianglesIsosceles Triangles
At least two sides are the same length
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Equilateral TrianglesEquilateral Triangles
All three sides are the same length
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Classifying TrianglesClassifying Triangles By Their Angles By Their Angles
AcuteRightObtuse
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Acute TrianglesAcute Triangles
Acute triangles have three acute angles
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Right TrianglesRight Triangles
Right triangles have one right angle
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Obtuse TrianglesObtuse Triangles
Obtuse triangles have one obtuse angle
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Classify this triangle.Classify this triangle.
Right Scalene
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Classify this triangle.Classify this triangle.
Obtuse Isosceles
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Classify this triangle.Classify this triangle.
Acute Scalene
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Classify this triangle.Classify this triangle.
Acute Isosceles
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Classify this triangle.Classify this triangle.
Obtuse Scalene
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Classify this triangle.Classify this triangle.
Right Isosceles
It’s YOUR Turn!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.
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Answer TimeAnswer Time
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1. Acute
2. Right
3. Obtuse
4. Acute
5. Obtuse6. Acute7. Right8. Obtuse
9. Acute
10. Acute Isosceles
11. Right Scalene
12. Obtuse Isosceles
13. Acute Equilateral
14. Obtuse Scalene
15. Right Scalene16. Acute Isosceles17. Obtuse Scalene
18. Acute Equilateral
Any Questions????Any Questions????
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Identifying TrianglesIdentifying 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 AnglesTriangles 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!!!
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Angle MeasuresAngle Measures
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60° + 60° + 60° = 180° 40° + 30° + 110° = 180°
ExamplesExamples
Will the following angle measures form a triangle?
1.) 80°, 40°, 60°
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YES!!!!!!!!!!!!YES!!!!!!!!!!!!80° + 40° + 60° = 180°
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ExamplesExamples
2.) 26°, 95°, 60°
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NO!!!!!!!!!!!!NO!!!!!!!!!!!!26° + 95° + 60° = 181°Remember, the sum of
all three angles MUST equal 180°!
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Side LengthsSide 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!
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Triangle Inequality TheoremTriangle Inequality Theorem
ExamplesExamples
Will the following side lengths form a triangle?
1.) 10 in, 12 in, 14 in
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YES!!!!!!!!!!!!YES!!!!!!!!!!!!10 + 12 > 1410 + 14 > 1212 + 14 > 10
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ExamplesExamples
2.) 2 cm, 8 cm, 16 cm
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NO!!!!!!!!!!!!!!!!!!NO!!!!!!!!!!!!!!!!!!2 + 8 < 162 + 16 > 88 + 16 > 2
Remember, ALL statements MUST BE TRUE for a triangle to be made!
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It’s YOUR Turn!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.
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Answer TimeAnswer Time
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1. Yes
2. No
3. No
4. Yes
5. Yes6. Yes
7. Yes
8. Yes
9. No
10. No
11. Yes
12. Yes
Any Questions????Any Questions????
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