Section 3.3 Triangles Thompson. Triangle Sum Theorem The sum of the measures --?--

Section 3.3Triangles

Thompson

Triangle Sum Theorem

The sum of the measures --?--.

The triangle angle sum theorem

• The sum of the measures of the angles of a triangle is 180.

• m<A + m<B + m<C = 180A

B C

83˚

45˚ x˚

Find the valueOf x

(4x+7)˚

(8x-1)˚

Find the valueOf x

Types of Triangles

• Equilateral– All sides congruent

• Isosceles– At least two sides are

congruent• Scalene

– No sides are congruent

“By Sides”

Page 133

Types of Triangles“By Angles”

• Equiangular– All angles are congruent

• Acute– All angles are acute (less than 90)

• Right– One right angle (90 )

• Obtuse– One obtuse angle (more than 90 less

than 180)

Classifying Triangles

Now we’re going to practice

“classifying triangles”

Both by “Sides” and by “Angles”

By Anglesequiangular

By Sidesequilateral

By Angles“Right”

By Sides“Scalene”

By Sides“Isosceles”

By Angles“Acute”

By Angles“Obtuse”

By SidesIsosceles

Definition:Exterior Angles of

Triangle• Exterior Angle– The angle formed by a side and an

extension of the side

• Remote Interior Angle– The two non-adjacent interior angles

Exterior Angle

Rem

ote

Inte

rior

Ang

les

Interior vs. Exterior AnglesAll the angles inside the triangle are

called interiorinterior angles. If you extend the sides of the triangle, then the angles that form a linear pair with the interior angles are called exteriorexterior angles.

Exterior Angle Theorem

• The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

• m<1 = m<2 + m<3

1

2

3

115˚ y˚

52˚

x˚

• The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.

• m<1 > m<2 AND m<1 > m<3

1

2

3

Corollary (free postulate)

SAT ExampleFind the

values of a, b, and c.

40

75

a

b

c

120

SAT Example

What is the value of c?

80

c

b

b

aa

“…This is pointless, when am I ever Going to run into a triangle in real life?!...”

Classwork 3.31-11 , 16-23, 31-36