Lesson 3-4 (Parallel & Perpendicular Lines)

perpendicular 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 G2Objectives: 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.

1 3

21

3

2

RemoteInterior Angles

ExteriorAngle

ExteriorAngle

Examples 3: Find the missing angle

78

50 1

110 62

2

Example 4:

x

Find x for the problem.

140

x

70

70

25

33

x

Example 5:

Find the measure of each numbered angle in the figure.

m 1 = 50 + 78 = 128Exterior Angle Theorem

m 2 = 180 - 128 = 52Supplementary Angles

m 3 = 120 - 52 = 68Exterior Angle Theorem

m 4 = 180 - 120 = 60Supplementary Angles

m 5 = 60 + 56 = 116Exterior Angle Theorem

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