Triangles Angles What do you know about triangles

Triangles & Angles

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 3 interior angles of a triangle add up to 180˚.

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 A subtract from 180˚. Find the measure of A. 90˚ C is 34˚ and B is right so =____. 124˚ 34˚+ 90˚ = ______ 180˚ - 124˚ = A B 34˚ C A = 56˚ Same answer if you write an equation and solve. 90 ˚ + 34 ˚ + x = 180 ˚ 124˚ + x = 180 ˚ x = 56˚ A = 56˚

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

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

Find the missing angle measurement: ∆HJK ~ ∆ MNP Find J H N J ? K M 85˚ 22˚ 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 107˚ 22 + 85 = ______ 73˚ 180 – 107 = ______ Angle N is 73˚, and J N so J = 73˚ J and N = ? ? P

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

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

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 The exterior angle adds up to the measure of 98 + 26. 98˚ It is 124˚. What is the measure of the missing angle in the triangle? Name two ways that you could figure that out. 56˚ 180 – 124 = ____ 26˚

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

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

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 . C B Z What is the measure of Z? 40 + 60 = 100 180 – 100 = 80˚ What is the measure of C? 40 + 60 = 100 180 – 100 = 80˚ Y Since C and Z have the same measure, we can conclude they are . If all three angles are , ∆ABC & ∆XYZ are similar triangles.