1. Triangles & Their Angles
Common Core Investigation 4: Geometry

2. What do you know about triangles?
Has 3 sides.
Some triangles are right, acute or obtuse.
Some triangles are equilateral, isosceles or scalene.
The 3 interior angles of a triangle add up to 180˚.

3. How do you find the missing angle of a triangle?
Remember the interior angles add up to 180˚.
If you know two angles, add them up and then subtract from 180˚.
34˚ C B A
Find the measure of A.
 C is 34˚ and B is right so =____.
90˚
34˚+ 90˚ = ______
124˚
180˚ - 124˚ = A
A = 56˚
Same answer if you write an equation and solve.
90 ˚ ˚ + x = 180 ˚
124˚ + x = 180 ˚
A = 56˚
x = 56˚

4. Find the missing angle measurement.
25˚
= _______
41˚
139˚
180 – 41 = _______
The missing angle is 139˚. ?
16˚

5. 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 X
The angles will be congruent (equal measures), but the side lengths will not
A   X C B
B   Y
C   Z Z Y

6. Find the missing angle measurement:
∆HJK ~ ∆ MNP M N P
22˚
85˚
Find  J H J K ?
Since the triangles are similar, the corresponding angles must be congruent (and will have equal angle measures)
H  M and K  P and  J  N
H and M = 22 ˚ and K and P = 85 ˚ and  J and N = ??
= ______
107˚
73˚
180 – 107 = ______
Angle N is 73˚, and  J  N so  J = 73˚

7. 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

8. Non-Adjacent Interior Angles of Triangles
non-adjacent interior angles are the two angles that are not adjacent to (next to) the exterior angle
also known as remote-interior angles
Non-adjacent interior angles
Exterior Angle

9. 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
Non-adjacent interior angles
98˚
The exterior angle adds up to the measure of
It is 124˚.
26˚
What is the measure of the missing angle in the triangle?
Name two ways that you could figure that out.
56˚
180 – 124 = ________

10. Find the missing angle measurement:
103 = 74 + ? ?
103˚
74˚

11. Find the missing angle measurement:
103 = 74 + ?
29 = ?
The missing angle is 29˚. ?
103˚
74˚

12. 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 X
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?
= 100
180 – 100 = 80˚ C B Z Y
Since C and Z have the same measure, we can conclude they are .
If all three angles are , ∆ABC & ∆XYZ are similar triangles.
What is the measure of Z?
= 100
180 – 100 = 80˚