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Chapter 4.1 Notes: Apply Triangle Sum Properties

Chapter 4.1 Notes: Apply Triangle Sum Properties. Goal: You will classify triangles and find measures of their angles. Classification By Sides. Classification By Angles. Classifying Triangles. Obtuse, Isosceles. Acute, Scalene. In classifying triangles, be as specific as possible.

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Chapter 4.1 Notes: Apply Triangle Sum Properties

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  1. Chapter 4.1 Notes: Apply Triangle Sum Properties Goal: You will classify triangles and find measures of their angles.

  2. Classification By Sides Classification By Angles

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

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

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

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

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

  8. What is the missing angle? 90º ? 30º ? + 180º 90º 30º 180 – 120 = 60˚

  9. What is the missing angle? ? 60º 60º ? + 60º 60º 180º 180-120 = 6060˚

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

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

  12. Ex.2: Classify the triangle shown in the diagram by its sides and angles.

  13. Ex.3: Classify the triangle by its sides and angles.

  14. Angles • When the sides of a polygon are extended, other angles are formed. • The original angles are the interior angles. • The angles that form linear pairs with the interior angles are the exterior angles.

  15. Theorem 4.2 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

  16. Ex.4: Find . Ex.5: Find the measure of in the diagram shown.

  17. A corollary to a theorem is a statement that can be proved easily using the theorem. • Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary.

  18. Ex.6: The tiled staircase shown forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other. Find the measure of each acute angle.

  19. Ex.7: Find Ex.8: Find the measure of each interior angle of ∆ABC, where

  20. Ex.9: Find the measures of the acute angles of the right triangle in the diagram shown.

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