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Triangle Sum Properties

Triangle Sum Properties. Classify triangles and find measures of their angles. A triangle is a polygon with three sides. A triangle with vertices A, B, and C is called “ triangle ABC ” or “ ∆ABC . ”. A. B. C. Classifying Triangles by Sides

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Triangle Sum Properties

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  1. Triangle Sum Properties Classify triangles and find measures of their angles.

  2. A triangleis a polygon with three sides. A triangle with vertices A, B, and C is called “triangle ABC” or “∆ABC.” A B C

  3. Classifying Triangles by Sides • A scalene triangle is a triangle with no congruent sides. • An isosceles triangle is a triangle with at least two congruent sides. • An equilateral triangle is a triangle with three congruent sides.

  4. Classifying Triangles by Angles • An acute triangle is a triangle with three acute angles. • A right triangle is a triangle with one right angle. • An obtuse triangle is a triangle with one obtuse angle. • An equiangular triangle is a triangle with three congruent angles.

  5. Classification By Sides Classification By Angles

  6. 1 3 2 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o. m<1 + m<2 + m<3 = 180°

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

  8. Property of triangles The sum of all the angles equals 180º degrees. 40º 90º 40º 50º + 180º 50º 90º

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

  10. Ex: 1What is the missing angle? 70º 70º x + x 180º 70º 70º 180– 140 = 40˚

  11. EX: 2 What is the missing angle? 90º x 30º x + 180º 90º 30º 180 – 120 = 60˚

  12. Ex: 3What is the missing angle? x 60º 60º x + 60º 60º 180º 180 – 120 = 60˚

  13. EX 4:What is the missing angle? X 30º 78º X + 78º 30º 180º 180 – 108 = 72˚

  14. What is the missing angle? ? 40º 40º ? + 40º 40º 180º 180 – 80 = 100˚

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

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