We reviewed a ton of terms that you knew from previous years:
- right angle
- acute angle
- obtuse angle
- straight angle
- reflex angle
- right triangle
- scalene triangle
- isoceles triangle
- equilateral/equiangular triangle
- hypotenuse (of a right triangle)
- median (of a triangle)
- perpendicular bisector :)
Those last few were the new learning today.
If a line has slope , any perpendicular line has slope , which is the negative reciprocal of .
If two perpendicular lines have slope and , then (if the lines aren’t horizontal and vertical).
A bisector is a line that intersects a line segment at its midpoint (cutting it into two equal pieces).
A perpendicular bisector is a line that intersects a line segment at its midpoint and is at 90 degress to that segment.
For example, suppose we have a segment with endpoints and .
The midpoint of that segment is . The slope of the segment is .
The perpendicular bisector passes through the point and has slope .
We can use the general form , substituting known values for , and :
and solve to get
Therefore the equation of the perpendicular bisector is .
No homework tonight.