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.

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?

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= 180 4x + 56= 180 4x = 124 x = 31

Find the Value for X 2x + 15 2x + 15 + 3x + 90 = 180 5x + 105 = 180 3x 5x = 75 x = 15

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

3x + 10 20 3x + 10 5x +16

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 46 o 3x + 13 8x - 1 2y o

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