Geometry 101

From November 2005:

Dave Adair and I recently had a riveting discussion regarding the new area behind the goal line where NHL Goalies are allowed to play the puck.

Dave: Hey Feisty, what’s that name of that shape defined by lines that begin six feet from either goal post and extend diagonally to points 28 feet apart at the endboards?

Feisty: Well Dave, I’m glad you asked. The shape is a four-sided polygon (quadrilateral) having exactly one pair of parallel sides, known as a Trapezoid.

Dave: I thought it was a Bermuda Rhombus.

Feisty: While the sum of all angles is 360 degrees for both the Trapezoid and the Rhombus, the Rhombus is a four-sided polygon having all four sides of equal length. It’s a common misnomer.

Dave: Must the opposite sides of a Trapezoid always be congruent too?
Feisty: They don't have to be.

Dave: Oh, so the other sides can look any way that you want them to?

Feisty: Right. However, the other sides cannot be parallel because we say that trapezoids have exactly one pair of parallel sides.

Dave: Yeah, because if it had 2 pairs of parallel sides then it would be a parallelogram!

Feisty: Very perceptive of you! Do you remember what we call a triangle that has two congruent sides?

Dave: An isosceles triangle?

Feisty: Right. So what do you think we call a trapezoid in which the two non-parallel sides are congruent?

Dave: An isosceles trapezoid?

Feisty: Fantabulous! Another beer?

Dave: Sure!