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Lesson 3-4 (Parallel & Perpendicular Lines) perpendicula r parallel

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3 Patterns (Perpendicular & Parallel) Theorem 3-7 If a // b b // c then a // c Theorem 3-8 If a ⊥ b b ⊥ c then a // c Theorem 3-9 If a ⊥ b b // c then a ⊥ c

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3.5 Parallel Lines and Triangles SOL G2 Objectives: TSW … use parallel lines to prove theorems about triangles To find measures of angles of triangles.

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Postulate 3.3 Parallel Postulate Through a point not on a line, there is one and only one line parallel to the given line. l There is exactly one line through P parallel to l.

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Theorem 3.10 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180° m ∠ A + m ∠ B + m ∠ C = 180 ° A BC

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Example 1: Find the missing angle measure. 58 39 83 35 24 18

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Example 2: Find the measures of the missing angles 1, 2, and 3.

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Definitions Exterior Angle of a Polygon – Remote Interior Angles - 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. 13 2 1 3 2 Remote Interior Angles Exterior Angle Exterior Angle

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Examples 3: Find the missing angle 78 50 1 110 62 2

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Example 4: x Find x for the problem. 140 x 70 25 33 x

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Example 5: Find the measure of each numbered angle in the figure. m 1 = 50 + 78 = 128 Exterior Angle Theorem m 2 = 180 - 128 = 52 Supplementary Angles m 3 = 120 - 52 = 68 Exterior Angle Theorem m 4 = 180 - 120 = 60 Supplementary Angles m 5 = 60 + 56 = 116 Exterior Angle Theorem

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Example 6: Find the measure of each numbered angle in the figure.

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Applying Triangle Sum Properties

Applying Triangle Sum Properties

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