Section 3-5 Parallel lines and Triangles.

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Presentation transcript:

Section 3-5 Parallel lines and Triangles. Michael Schuetz

Postulate 3-2: Parallel Postulate. Though a point not on a line, there is one and only one line parallel to the given line. Point P is not on line a so there is only one line that goes through point P that is parallel to line a.

Theorem 3-11: Triangle Angle-Sum Theorem. The sum of the measures of the angles of a triangle is 180˚.

Example 1, Angle Measure What are the measures of the missing angles in the picture below? 43˚ 59˚ 49˚ x˚ y˚ z˚

Definitions Exterior angle of a polygon is an angle 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. Remote interior Angles Side Exterior Angle Extended side

Theorem 3-12: 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.

Example 2, Using the triangle exterior angle theorem. What is the measure of angle 1? What is the measure of angle 2? 80˚ 18˚ 1 124˚ 59˚ 2

Homework: P. 175, #’s 12-15, 22-24, 29-32