Triangles

04/18/23Geometry1

2

Two Ways to Classify TrianglesTwo Ways to Classify Triangles

By Their SidesBy Their Angles

3

Classifying Triangles Classifying Triangles By Their SidesBy Their Sides

Scalene IsoscelesEquilateral

Types of TrianglesTypes of Triangles

Scalene triangle: A triangle that has no congruent (equal) sides

5

Scalene TrianglesScalene Triangles

No sides are the same length

Types of TrianglesTypes of Triangles

Isosceles triangle: A triangle with at least two congruent (equal) sides

7

Isosceles TrianglesIsosceles Triangles

At least two sides are the same length

Types of TrianglesTypes of Triangles

Equilateral triangle: A triangle with three congruent (equal) sides and three equal angles

These marks indicate equality.

9

Equilateral TrianglesEquilateral Triangles

All three sides are the same length

Types of TrianglesTypes of Triangles

Name each type of triangle

1

2

3

4

Types of TrianglesTypes of Triangles

Name each type of triangle

1

2

3

4

Equilateral

Right

Isosceles

Scalene

12

Classifying TrianglesClassifying Triangles By Their Angles By Their Angles

AcuteRightObtuse

13

Acute TrianglesAcute Triangles

Acute triangles have three acute angles

14

Right TrianglesRight Triangles

Right triangles have one right angle

Types of TrianglesTypes of Triangles

Right triangle: Has only one right angle (90 degrees)

This box indicates a right angle or a 90-degree angle.

16

Obtuse TrianglesObtuse Triangles

Obtuse triangles have one obtuse angle

17

Classify this triangle.Classify this triangle.

Right Scalene

18

Classify this triangle.Classify this triangle.

Obtuse Isosceles

19

Classify this triangle.Classify this triangle.

Acute Scalene

20

Classify this triangle.Classify this triangle.

Acute Isosceles

21

Classify this triangle.Classify this triangle.

Obtuse Scalene

22

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.

23

Answer TimeAnswer Time

24

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

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!!!

25

Angle MeasuresAngle Measures

26

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

ExamplesExamples

Will the following angle measures form a triangle?

1.) 80°, 40°, 60°

27

YES!!!!!!!!!!!!YES!!!!!!!!!!!!80° + 40° + 60° = 180°

28

ExamplesExamples

2.) 26°, 95°, 60°

29

NO!!!!!!!!!!!!NO!!!!!!!!!!!!26° + 95° + 60° = 181°Remember, the sum of

all three angles MUST equal 180°!

30

Interior AnglesInterior Angles

Interior angles: An interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint

Interior angles of a triangle always equal 180 degrees.

Measuring AnglesMeasuring AnglesYou measure angles with a protractor.

This point goes at the vertex of the angle

This point is 0

This point is 0.

Notice there are two scales. Be careful which 0 you start at.

900