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4.1  Apply Triangle Sum Theorems

4.1  Apply Triangle Sum Theorems. Triangles Goals today…. Classify triangles by sides and angles Find angle measures in triangles. Classification by sides. Equilateral has all sides congruent Isosceles has 2 congruent sides Scalene has no congruent sides.

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4.1  Apply Triangle Sum Theorems

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  1. 4.1 Apply Triangle Sum Theorems

  2. TrianglesGoals today…. • Classify triangles by sides and angles • Find angle measures in triangles

  3. Classification by sides • Equilateral has all sides congruent • Isosceles has 2 congruent sides • Scalene has no congruent sides

  4. Classification by Angles • Acute has 3 angles each less than 90° • Right triangle has one angle = 90 ° • Obtuse has 1 angle > 90 ° • Equiangular: has three congruent angles

  5. Right, Scalene Triangle

  6. Right, Isosceles Triangle

  7. Scalene, Obtuse Triangle

  8. Classify PQOby its sides. Then determine if the triangle is a right triangle. EXAMPLE 2 Classify a triangle in a coordinate plane

  9. Triangle Sum TheoremThe sum of the measures of the interior angles of a triangle is 180°. B A C mA + mB +mC = 180°

  10. 32 y x 50

  11. Exterior s (4, 5, and 6) 4 2 3 1 6 5 Interior Angles (1, 2, and 3)

  12. Exterior Angle TheoremThe measure of the exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles mD = mB + mC B C D A

  13. Findm∠ JKM. ALGEBRA EXAMPLE 3 Find an angle measure

  14. A#30:Page 221,#2-16 even, 17-37all

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