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Applying Triangle Sum Properties

- Section 4.1

Triangles

- Triangles are polygons with three sides.
- There are several types of triangle
- Scalene
- Isosceles
- Equilateral
- Equiangular
- Obtuse
- Acute
- Right

Scalene Triangles

- Scalene triangles do not have any congruent

sides. - In other words, no side has the same length.

6cm

3cm

8cm

Isosceles Triangle

- A triangle with 2 congruent sides.
- 2 sides of the triangle will have the same

length. - 2 of the angles will also have the same angle

measure.

Equilateral Triangles

- All sides have the same length

Equiangular Triangles

- All angles have the same angle measure.

Acute Triangle

- All angles are acute angles.

Right Triangle

- Will have one right angle.

Obtuse Angle

- Will have one obtuse angle.

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- 1 - 10

Exterior Angles vs. Interior Angles

- Exterior Angles are angles that are on the

outside of a figure. - Interior Angles are angles on the inside of a

figure.

Interior or Exterior?

Interior or Exterior?

Interior or Exterior?

Triangle Sum Theorem (Postulate Sheet)

- States that the sum of the interior angles is

180. - We will do algebraic problems using this theorem.

The sum of the angles is 180, so x 3x 60

180

4x 60 180

4x 120

x 30

Find the Value for X

2x 15 3x 90 180

2x 15

5x 105 180

5x 75

3x

x 15

Corollary to the Triangle Sum Theorem (Postulate

Sheet)

- Acute angles of a right triangle are

complementary.

3x 10

3x 10 20 90

3x 30 90

20

3x 60

x 20

Exterior Angle Sum Theorem

- The measure of the exterior angle of a triangle

is equal to the sum of the non-adjacent interior

angles of the triangle

88 70 y

158 y

- 2x 40 x 72

- 2x x 32

- x 32

Find x and y

38 7x 1 10x 9

10 x

39 7x 10x 9

10x 9

109

10(10) 9

39 3x 9

100 9

30 3x

109

10 x

109 y 180

y 71

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