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

2. 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˚.

3. 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. C B A  C is 34˚ and  B is ________. 34˚+ 90˚ = ______ 124˚ 180˚ - 124˚ =  A  A = 56˚

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

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 B C X YZ  A   X  B   Y  C   Z

6. 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 B C 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 = 100 180 – 100 = 80˚ What is the measure of  Z? 40 + 60 = 100 180 – 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.

7. Find the missing angle measurement: ∆HJK ~ ∆ MNP H J K M N P 22˚ 85˚ ?  H   M and  K   P  J   N How can you find  J? 22 + 85 = ______ 107˚ 180 – 107 = ______ 73˚  J = 73˚

8. 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

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 (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

10. 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

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