Transcript 3-5 Parallel Lines and Triangles.ppt

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
3 acute angles
3 congruent angles
Right Triangle
Obtuse Triangle
1 right angle
1 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?