3 5 Parallel Lines and Triangles 1 Objectives

3. 5 Parallel Lines and Triangles 1

Objectives To use parallel lines to prove a theorem about triangles To find measures of angles in triangles

Parallel Postulate 3. 3 Through a point not on a line, there is one and only one line parallel to the given line Not Parallel l P

Triangle Sum Theorem 3. 10 – the sum of the measures of the angles of a triangle is 180

Proof of Triangle Sum Theorem 1 11 22 3 3 3 Alternate Interior Angles

Example Solve for the angles of the triangle.

Example Solve for the angles of the triangle

Exterior Angles of Triangle Exterior Angles – angle formed by a side and an extension of an adjacent side straight angle = 180 3 1 <1, <2, and <3 are Exterior Angles 2 The Exterior angles are not the straight angles!!!

Remote Interior Angles Remote Interior angles – the two nonadjacent angles to an exterior angle 3 4 6 1 5 Exterior Angle Remote Interior Angles <1 <4 and <5 <2 <4 and <6 <3 <5 and <6 2

Triangle Exterior Angle Theorem 3. 11 – the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles 4 1 5

Example What is the value of x?

Example Find the measure of each angle.

Example What is the value of x?

Take Home Message Interior Angles of a Triangle Sum is 180 Exterior Angles of a Triangle Exterior Angles EQUALS the sum of the two remote interior angles