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3.5 Parallel Lines and Triangles

3.5 Parallel Lines and Triangles. Objectives. To use parallel lines to prove a theorem about triangles To find measures of angles in triangles. Parallel Postulate. 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.

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3.5 Parallel Lines and Triangles

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  1. 3.5 Parallel Lines and Triangles

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

  3. Parallel Postulate • 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

  4. Triangle Sum Theorem • Theorem 3.10 – the sum of the measures of the angles of a triangle is 180

  5. Proof of Triangle Sum Theorem 3 1 2 1 3 2 Alternate Interior Angles 1 3

  6. Example Check Work • Solve for the angles of the triangle.

  7. Example Check Work • Solve for the angles of the triangle

  8. 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!!!

  9. Remote Interior Angles • Remote Interior angles – the two nonadjacent angles to an exterior angle 4 6 3 1 5 2

  10. Triangle Exterior Angle Theorem • Theorem 3.11 – the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles 1 4 5

  11. Example • What is the value of x?

  12. Example • Find the measure of each angle.

  13. Example • What is the value of x?

  14. 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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