Download Geometry: Section 3.4 Proofs with Perpendicular Lines

Geometry: Section 3.4
Proofs with Perpendicular Lines
What you will learn:
1. Find the distance form a point to a line
2. Construct perpendicular segments
3. Prove theorems about perpendicular lines
4. Solve real life problems about perpendicular
lines
The distance from a point to a line is the
length of the perpendicular segment from the
point to the line.
This perpendicular segment will be
the shortest distance from the point to the line
x1  x2    y1  y2 
2
2
AC 
 3  1  3  1
AC 
 4  4
2
2
2
2
AC  16  16  32
Constructing Perpendicular Lines
Example: Construct a line through point A
that will be perpendicular to line m.
The perpendicular bisector of a segment is a
line which is perpendicular to the segment at
its midpoint.
Constructing a Perpendicular Bisector
Example: Construct the perpendicular
bisector of the segment.
The following theorems all deal with perpendicular lines.
1)h || k , j  h
2)2 is a right angle
1)Given
2) Def. of Perpendicular
3)m2  90
3) Def. of Right Angle
4)m2  m6
4) Correponding Angles Theorem
)m6  90
5) Substitution
)6 is a right angle
) Def. of Right Angle
)jk
) Def. of Perpendicular
HW: pp 152 – 154 / 3 – 5, 10, 16, 17 – 20, 25