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isosceles triangle
triangle with two equal sides, distance
equilateral triangle
a triangle with three equal sides, distance
right triangle
a triangle with one right angle, slope
rhombus
a quadrilateral with four equal sides, distance
square
a quadrilateral with four equal sides and one right angle, distance and slope
parallelogram
a quadrilateral with two pairs of opposite parallel angles, slope
rectangle
a quadrilateral with two pairs of opposite parallel sides and one right angle, slope
trapezoid
a quadrilateral with one pair of opposite parallel sides and one right angle, slope
isosceles trapezoid
a quadrilateral with one pair of opposite parallel sides and one pair of opposite not parallel sides and two equal sides, slope and distance
to prove equal sides
distance formula
to prove parallel sides and right angles
slope formula