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} .

perpendicularBisector

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.

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