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Classifying Triangles and Angle Properties in Geometry

Learn about triangle sum properties, classification by sides and angles, and angle measurement theorems in this comprehensive geometry lesson. Practice identifying obtuse, isosceles, acute, and scalene triangles. Understand the Triangle Sum Theorem and its applications. Explore exterior and interior angles, as well as their relationships. Solve angle measurement problems and apply corollaries to triangle properties.

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Classifying Triangles and Angle Properties in Geometry

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  1. 10/13/14 Geometry Bellwork

  2. 4.1 Apply Triangle Sum Properties 10/13/14 (Starts on Page 217 in book)

  3. Classification By Sides Classification By Angles

  4. Classifying Triangles In classifying triangles, be as specific as possible. Obtuse, Isosceles Acute, Scalene

  5. 1 3 2 Theorem 4.1 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o. m<1 + m<2 + m<3 = 180°

  6. Property of triangles The sum of all the angles equals 180º degrees. 60º 90º 30º + 60º 180º 30º 90º

  7. Property of triangles The sum of all the angles equals 180º degrees. 60º 60º 60º 60º + 180º 60º 60º

  8. What is the missing angle? 70º 70º ? ? + 180º 70º 70º 180 – 140 = 40˚

  9. What is the missing angle? ? 30º 78º ? + 78º 30º 180º 180 – 108 = 72˚

  10. Find all the angle measures 35x 45x 10x 180 = 35x + 45x + 10x 180 = 90x 2 = x 90°, 70°, 20°

  11. What can we find out? The ladder is leaning on the ground at a 75º angle. At what angle is the top of the ladder touching the building? 180 = 75 + 90 + x 180 = 165 + x 15˚ = x

  12. Exterior Angles vs. Interior Angles Exterior Angles are angles that are on the outside of a figure. Interior Angles are angles on the inside of a figure.

  13. Theorem 4.2 Exterior Angle Sum Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle

  14. Find measure of angle y 88 + 70 = y 158 = y

  15. Find the value of x • 2x = x + 32 • x = 32 2x + 40 = x + 72

  16. Corollary to Triangle Sum Theorem ACorollaryis a statement that readily follows from a theorem. The acute angles of a right triangle are complementary. m∠A + m∠B = 90o

  17. 10/13/14 Geometry Homework Textbook: Page: 221 Exercises: 1-6 All, 14-19 All Due 10/14/14

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