Triangles: Angle Sum & Classifying Triangles

Tutorial 12b

The Triangle Angle-Sum Theorem

The interior angles of any triangle have a sum of 180.

A

B

C

mA + mB + mC = 180

Example Problems: Find the missing angles.

x 33

117 x = 180 – (117 + 33)

w

t

30

t =

w =

60 60

y =

z =

88

92

z 47

45

y

=30

Exterior Angles of a Triangle

An exterior angle of a polygon is an angle formed by a side and an extension of a side. For each exterior angle of a triangle, the two non-adjacent interior angles are called its remote interior angles.

3

1

2

Remote Interior Angles are

Exterior Angle is 1

2 and 3

Exterior Angle Theorem

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

2

31

m1 = m2 + m3

Corollary: Exterior Angle Theorem

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

2

31

m1 > m2 and m1 > m3

Classifying Triangles: By Side Lengths

Equilateral

All sides congruent

Isosceles

At least two sides congruent

Scalene

No sides congruent

Classifying Triangles: By Angle Measure

Equiangular

All angles congruent

Acute

All angles acute

Obtuse

One obtuse angleRight

One right angle

If you cannot remember the types of angles click here. Review

A little more about Right Triangles

• In a right triangle, the side opposite the right angle is the longest side. It is the called the hypotenuse.

• The other two sides are called the legs of a right triangle.

b

ca

Side c is the hypotenuse, and is the longest side.

Sides a and b are the legs of the triangle.

Angles less than 90° are called Acute Angles.

Angles equal to 180° are called Straight Angles.

Angles equal to 90° are called Right Angles.

Classifying AnglesClassifying Angles

Acute Angle: Obtuse Angle:

Right Angle: Straight Angle:

Types of Angles:Types of Angles:

Angles greater than 90° are called Obtuse Angles.

Symbol for right angle

180°

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