The segment that connects the midpoints of the legs of a trapezoid is called the . This segment’s length is always equal to one-half the sum of the trapezoid’s bases, or
mid-segment
It follows that the area of a trapezoid is equal to the length of this mid-segment multiplied by the height:
so, the area of a trapezoid is given by
Isosceles Trapezoids
Definition: An is a trapezoid whose legs are congruent.
There are several theorems we can use to help us prove that a trapezoid is isosceles. These properties are listed below.
(1) A trapezoid is isosceles if and only if the base angles are congruent.
(2) A trapezoid is isosceles if and only if the diagonals are congruent.
(3) If a trapezoid is isosceles, then its opposite angles are supplementary.
Kites or deltoids
Definition: A is a quadrilateral with two distinct pairs of adjacent sides that are congruent.
Recall that parallelograms also had pairs of congruent sides. However, their congruent sides were always opposite sides. Kites have two pairs of congruent sides that meet at two different points.
Kites have a couple of properties that will help us identify them from other quadrilaterals.
(1) The diagonals of a kite meet at a right angle.
(2) Kites have exactly one pair of opposite angles that are congruent.
Is a trapezoid a kite?
answer is:
In general, a trapezoid is a figure with of sides.
The kite is a figure with of , each pair being of different length.
You can picture the kite by picturing the "traditional" kind of kite that flies. It is an "enlongated diamond" with the lower pair of sides longer than the top pair. Nowhere in the formula for a kite is there a provision for any two sides to be parallel. There cannot be. So a trapezoid, which has a pair of parallel sides, can't be a kite.
