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3-5 Parallel Lines and Triangles

3-5 Parallel Lines and Triangles. Classification by Sides (NOT in the book!). Equilateral Triangle. Isosceles Triangle. 3 congruent sides. 2 congruent sides. Scalene Triangle. No congruent sides. Classification by Angles (NOT in the book!). Acute Triangle. Equiangular Triangle.

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3-5 Parallel Lines and Triangles

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  1. 3-5 Parallel Lines and Triangles

  2. Classification by Sides(NOT in the book!) Equilateral Triangle Isosceles Triangle 3 congruent sides 2 congruent sides Scalene Triangle No congruent sides

  3. Classification by Angles(NOT in the book!) Acute Triangle Equiangular Triangle 3 acute angles 3 congruent angles Right Triangle Obtuse Triangle 1 right angle 1 obtuse angle

  4. Triangle Angle-Sum Theorem • The sum of the measures of the angles of a triangle is 180.

  5. Using the Triangle Angle-Sum Theorem • What are the values of x, y, and z?

  6.  Solve for x, y, and z.

  7. Angles in Triangles • An exterior angle is formed by a side and an extension of an adjacent side. • For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles. Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. m1 = m2 + m3

  8. Using the Triangle Exterior Angle Theorem • What is the measure of 1? • What is the measure of 2?

  9.  Two angles of a triangle measure 53. What is the measure of an exterior angle at each vertex of the triangle?

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