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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