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.

3cm

8cm

6cm

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.

Obtuse Angle Will have one obtuse angle.

Acute Triangle All angles are acute angles.

Right Triangle Will have one right angle.

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 + 56= 1804x + 56= 180

4x = 124x = 31

Find the Value for X

2x + 15

3x

2x + 15 + 3x + 90 = 180

5x + 105 = 180

5x = 75

x = 15

Corollary to the Triangle Sum Theorem (Postulate Sheet) Acute angles of a right triangle are

complementary.

3x + 10

5x +16

3x + 10

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

3x + 13

46o

8x - 1

2yo

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