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Triangle Classification and Measures

Learn how to classify triangles by sides and angles, calculate missing angles, explore interior and exterior angles, and understand important theorems related to triangles.

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Triangle Classification and Measures

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  1. Classifying Triangles Angle Measures of Triangles

  2. Triangle • A triangle is a figure formed by three segments joining three noncollinear points.

  3. Classifying Triangles by Sides • Equilateral Triangle • Isosceles Triangle • Scalene Triangle

  4. Equilateral Triangle • An equilateral triangle has three congruent sides.

  5. Isosceles Triangle • An isosceles triangle has at least two congruent sides.

  6. Scalene Triangle • A scalene triangle has no congruent sides.

  7. Classify the triangle by its sides.

  8. Classification of Triangles by Angles • Equiangular triangle • Acute triangle • Right triangle • Obtuse triangle

  9. Equiangular Triangle • An equiangular triangle has three congruent angles.

  10. Acute Triangle • An acute triangle has three acute angles.

  11. Right Triangle • A right triangle has one right angle.

  12. Obtuse Triangle • An obtuse triangle has one obtuse angle

  13. Classify the triangle by its angles.

  14. Vertex • A vertex of a triangle is a point that joins two sides of the triangle. • The side across from an angle is the opposite side.

  15. Name the side that is opposite the angle. • Angle J • Angle K • Angle L

  16. Triangle Sum Theorem • The sum of the measures of the angles of a triangle is 180º. • In ΔABC, mA + m B + m C = 180º

  17. Find the measure of the missing angle.

  18. Corollary to the Triangle Sum Theorem • The acute angles of a right triangle are complementary. • In ΔABC, if m  C = 90º, then m  A + m B= 90º A B C

  19. ΔABC is a right triangle. Find the measure of angle A.

  20. Interior Angles • When the sides of a triangle are extended, other angles are formed. • The three original angles are the interior angles.

  21. Exterior Angles • The angles that are adjacent to the interior angles are the exterior angles. • It is common to show only one exterior angle at a vertex.

  22. Exterior Angles Theorem • The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. • m 1 = m A + m B

  23. Find the measure of angle 1.

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