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Triangles & Their Angles

Triangles & Their Angles. Common Core Investigation 4: Geometry. Learning Goal 3(8.G.A.5): The student will understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. What do you know about triangles?. Has 3 sides.

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Triangles & Their Angles

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

  2. Learning Goal 3(8.G.A.5): The student will understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software.

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

  4. 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˚. A Find the measure of A.  C is 34˚ and B is ________. 124˚ 34˚+ 90˚ = ______ 34˚ 180˚ - 124˚ = A B C A = 56˚

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

  6. 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 A   X B   Y C   Z C B Z Y

  7. 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? 40 + 60 = 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? 40 + 60 = 100 180 – 100 = 80˚

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

  9. 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

  10. 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). Non-adjacent interior angles 98˚ The exterior angle adds up to the measure of 98 + 26. 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 = ________

  11. 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/triangleextangletheorem.html

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

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