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
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