3-5 Parallel Lines and Triangles. Classification by Sides (NOT in the book!) Equilateral TriangleIsosceles Triangle Scalene Triangle 3 congruent sides2.

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Presentation transcript:

3-5 Parallel Lines and Triangles

Classification by Sides (NOT in the book!) Equilateral TriangleIsosceles Triangle Scalene Triangle 3 congruent sides2 congruent sides No congruent sides

Classification by Angles (NOT in the book!) Acute TriangleEquiangular Triangle Right TriangleObtuse Triangle 3 acute angles3 congruent angles 1 right angle1 obtuse angle

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

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

 Solve for x, y, and z.

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

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

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