# MPM2D Geometry terms – 2015-10-19

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)
• vertex
• side
• altitude
• perpendicular
• bisector
• perpendicular bisector :)

Those last few were the new learning today.

If a line has slope $m_1$, any perpendicular line has slope $-\frac{1}{m_1}$, which is the negative reciprocal of $m_1$.

If two perpendicular lines have slope $m_1$ and $m_2$, then $m_1 \times m_2 = -1$ (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 $(4,9)$ and $(8,3)$.

The midpoint of that segment is $(\frac{4+8}{2},\frac{9+3}{2}) = (6,6)$. The slope of the segment is $m_1=\frac{3-9}{8-4}=-\frac{3}{2}$.

The perpendicular bisector passes through the point $(6,6)$ and has slope $m_2=\frac{2}{3}$.

We can use the general form $y=mx+b$, substituting known values for $m_1$, $x$ and $y$:

$6 = \frac{2}{3}(6) + b$

and solve to get

$b=2$

Therefore the equation of the perpendicular bisector is $y=\frac{2}{3}x + 2$.

No homework tonight.