Triangles & Their AnglesCommon Core Investigation 4: Geometry

What do you know about triangles?1. Has 3 sides.2. Some triangles are right,

acute or obtuse.3. Some triangles are

equilateral, isosceles or scalene.

4. The angles of a triangle add up to 180˚.

How do you find the missing angle of a triangle?• Remember all triangles add up to 180˚.• If you know two angles, add them up and then

subtract from 180˚.

34˚

Find the measure of A.

CB

A

C is 34˚ and B is ________.

34˚+ 90˚ = ______124˚

180˚ - 124˚ = A

A = 56˚

Find the missing angle measurement.

16˚

25˚

?

16 + 25 = _______41˚

180 – 41 = _______139˚

Similar Triangles• Similar means same shape but not the same size.• Similar triangles are the same shape but different sizes.• Corresponding angles in similar triangles are congruent.

• Triangle ABC is similar to Triangle XYZ. (∆ABC ~ ∆XYZ)

A

BC

X

YZ

A XB Y

C Z

Angle-Angle Criterion for Similarity of Triangles• How do we know that all of the angles of the two triangles

really are congruent?• Let’s look at ∆ABC & ∆XYZ again.

A

BC

X

YZ

If A is 40˚ and X is 40 ˚ they are .

If B is 60˚ and Y is 60 ˚ they are .

What is the measure of C?40 + 60 = 100180 – 100 = 80˚

What is the measure of Z?40 + 60 = 100180 – 100 = 80˚

Since C and Z have the same measure, we can conclude they are .If all three angles are , ∆ABC & ∆XYZ are similar triangles.

Find the missing angle measurement:

∆HJK ~ ∆ MNP

H

J

K

M

N

P22˚ 85˚

?

H M and K P

J N

How can you find J?

22 + 85 = ______107˚

180 – 107 = ______73˚

J = 73˚

Exterior Angles of Triangles• An exterior angle is formed by one side of a triangle and the

extension of an adjacent side of the triangle.• (adjacent means next to)

Exterior Angle

Exterior Angles of Triangles• The measure of an exterior angle of a triangle is equal to the

sum of the measures of the two non-adjacent interior angles (also known as remote-interior angles).

98˚

26˚

The exterior angle adds up to the measure of 98 + 26.

It is 124˚.

What is the measure of the missing angle in the triangle?Name two ways that you could figure that out.

180 – 124 = ________56˚

Non-adjacent interior angles

Exterior Angles of Triangles• Use the link below to see how the exterior angle is related to

the 2 non-adjacent interior angles.• http://www.mathopenref.com/triangleextangle.html

Find the missing angle measurement:

74˚103˚

? 103 = 74 + ?-74 -7429 = ?The missing angle is 29˚.