Section 3.6 – Prove Theorems About
Perpendicular Lines
Section 3.6 – Prove Theorems About
Perpendicular Lines
Example 1:
In the diagram below, Line AB is perpendicular
to Line BC. What can you conclude about <1
and <2?
Section 3.6 – Prove Theorems About
Perpendicular Lines
Section 3.6 – Prove Theorems About
Perpendicular Lines
Example 2:
Prove that if two sides of two adjacent angles
are perpendicular, then the angles are
complementary.
Given: Ray ED is perp to Ray EF
Prove: <7 and <8 are complementary
Section 3.6 – Prove Theorems About
Perpendicular Lines
Section 3.6 – Prove Theorems About
Perpendicular Lines
Example 3:
Determine which lines, if any, must be parallel
in the diagram. Explain you reasoning.
Section 3.6 – Prove Theorems About
Perpendicular Lines
Distance From a Line
The distance from a point to a line is the
length of the perpendicular segment from the
point to the line. This perpendicular segment is
the shortest distance between the point and the
line. For example, the distance between point
A and line k is AB.
Section 3.6 – Prove Theorems About
Perpendicular Lines
Distance From a Line
The distance between two parallel lines is
the length of any perpendicular segment joining
the two lines. For example, the distance
between line p and line m is CD or EF.
Section 3.6 – Prove Theorems About
Perpendicular Lines
Example 4:
a. What is the distance from point A to line c?
b. What is the distance from line c to line d?
Section 3.6 – Prove Theorems About
Perpendicular Lines
Example 5:
Graph the line y = x + 1. What point on the line
is the shortest distance from the point
(4, 1)?
What is the distance? Round to the nearest
tenth.