MPM2D – Properties of Triangles and Quadrilaterals
Type of Triangle
Equilateral Triangle
Properties
All sides and all angles are equal.
How can I determine if a shape is one?
Use the distance formula to find the length of all sides; if all
sides are equal, it is equilateral.
Isosceles Triangle
Two sides and two angles are equal.
Use the distance formula to find the length of all sides; if two
sides are equal (and the third is a different length,) it is
isosceles.
Scalene Triangle
No sides and no angles are equal.
Use the distance formula to find the length of all sides; if none
are equal, it is a scalene triangle.
Right Triangle
The triangle has one right angle.
Use the slope formula to determine the slope of each side; if
two of the slopes are opposite reciprocals, then it is a right
triangle.
Type of Quadrilateral
Parallelogram
Properties
Opposite sides are parallel and equal in
length.
Rhombus
All sides are equal in length. There are
two pairs of parallel sides.
Rectangle
Opposite sides are parallel and equal in
length. Adjacent (intersecting) sides
meet at a 90˚ angle.
Square
All sides are equal. There are 2 pairs of
parallel sides. Adjacent (intersecting)
sides meet at a 90˚ angle.
Trapezoid
One (and only one) set of opposite
parallel sides.
If two sides are equal in length, it is an
isosceles trapezoid.
How can I determine if a shape is one?
1. Use the distance formula to determine the length of each side.
You will need to find two pairs of equal (and opposite) sides.
AND
2. Use the slope formula to determine the slope of each side. If
opposite sides have the same slope, they are parallel.
1. Use the distance formula to determine the length of each side.
You will need to find all sides having equal length.
AND
2. Use the slope formula to determine the slope of each side. If
opposite sides have the same slope, they are parallel.
1. Use the distance formula to determine the length of each side.
You will need to find two pairs of equal (and opposite) sides.
AND
2. Use the slope formula to determine the slope of each side. If
opposite sides have the same slope, they are parallel.
AND
3. You also want two sets of slopes which are opposite
reciprocals, meaning that you have perpendicular lines.
1. Use the distance formula to determine the length of each side.
You will need to find all sides having equal length.
AND
2. Use the slope formula to determine the slope of each side. If
opposite sides have the same slope, they are parallel.
AND
1. You also want two sets of slopes which are opposite
reciprocals, meaning that you have perpendicular lines.
1. Use the slope formula to determine the slope of each side. If
opposite sides have the same slope, they are parallel.