lesson 3-4 (parallel & perpendicular lines) perpendicula r parallel
TRANSCRIPT
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
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
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