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

## Presentation on theme: "Lesson 3-4 (Parallel & Perpendicular Lines) perpendicula r parallel."— Presentation transcript:

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

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

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.

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.

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

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

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

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

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

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

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

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