Triangle Sum Theorem&

Exterior Angle Theorem

Work in groups to answer the questions. Try your best.

1. Name 2 pair of alternate interior angles5 & 3 and 4 & 1

2. What is the sum of m1 + m2 + m3? 180°

3. If m4 = 65° and m5 = 50°, what is m2?

65°

1 32

4 5

4. Find all the angle measures50°

40°

90°

40° 40°

90° 130°

50°

50°

Vocabulary

• Adjacent angles – angles that share a common vertex and side

• Vertical angles – a pair of non-overlapping angles that are opposite and congruent to each other when two lines intersect

• Complementary angles – two angles whose sum of angle measures equals 90 degrees

• Supplementary angles – two angles whose sum of angle measures equals 180 degrees

• Congruent angles – angles whose angle measurements are equal

continued . . .• Axes – the vertical and horizontal lines that act as a

reference when plotting points on a coordinate plane• Exterior angles of a triangle – angles that are outside

of a triangle between one side of a triangle and the extension of the adjacent side

• Interior angles of a triangle – angles that are inside of a triangle, formed by two sides of the triangle

• Transversal – a line that intersects two or more lines• Angle-angle criterion for triangles – if two angles in

one triangle are congruent to two angles in another triangle, then the measure of the third angle in both triangles are congruent

Objectives---What we’ll learn…

• Find the measurement of a missing angle by using Triangle Angle Sum Theorem.

• Find the measurement of a missing angle by using Exterior Angle Theorem.

Triangle Sum Theorem

The sum of the angle measures in a triangle equal 180°

32

1

1 + 2 + 3 = 180°

Isosceles Triangles

2 congruent sides 2 congruent base angles

Isosceles Triangles & Angle Sum Theorem

E + W + H = 180o

W H

E + 2(W) = 180o

Base Angles are congruent.

Exterior Angle Theorem

The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles

exterior angle

remote interior

angles

A = C + D

Exterior Angle Theorem

The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles

3

2

1 4

exterior angle

remote interior

angles

4 = 1 + 2

Example 1 on Exterior Angle

Example 2 on Exterior Angle

Shortcut:

Interior 1 + Interior 2 + Interior 3 = 1800

= 1800

1. Triangle INTERIOR Angle Sum

2. Triangle EXTERIOR Angle Sum

Remote Interior 1

+ Remote Interior 2 = Exterior Angle

= Exterior Angle

an example with numbers

x

82°

30° y

find x & y

x = 68°

y = 112°

60º 42º y

X