# Parallel And Perpendicular Lines Worksheet Page 36

Perpendiculars and Distance
Find the distance between a point and a line.
Find the distance between parallel lines.
Vocabulary
does the distance between
does the distance between
parallel lines relate to
parallel lines relate to
equidistant
hanging new shelves?
hanging new shelves?
When installing shelf brackets, it is
important that the vertical bracing be
parallel in order for the shelves to line
up. One technique is to install the first
brace and then use a carpenter’s square to measure and mark two or more
points the same distance from the first brace. You can then align the second
brace with those marks.
DISTANCE FROM A POINT TO A LINE
In Lesson 3-5, you learned that if
two lines are perpendicular to the same line, then they are parallel. The carpenter’s
square is used to construct a line perpendicular to each pair of shelves. The space
between each pair of shelves is measured along the perpendicular segment. This
is to ensure that the shelves are parallel. This is an example of using lines and
perpendicular segments to determine distance. The shortest segment from a point
to a line is the perpendicular segment from the point to the line.
Distance Between a Point and a Line
• Words
• Model
C
The distance from a line to
shortest
a point not on the line is
distance
the length of the segment
perpendicular to the line
from the point.
A
B
Study Tip
Distance from a Point to a Line
Example
Example
1
1
Measuring the
Shortest Distance
Draw the segment that represents
P
You can use tools like the
the distance from P to AB.
corner of a piece of paper
or your book to help draw
A
B
a right angle.
Since the distance from a line to a point not on the line is
P
the length of the segment perpendicular to the line from
the point, extend AB and draw PQ so that PQ
AB.
A
B
Q
When you draw a perpendicular segment from a point to a line, you can
guarantee that it is perpendicular by using the construction of a line perpendicular
to a line through a point not on that line.
Lesson 3-6 Perpendiculars and Distance 159
Aaron Haupt