Trapezoids and Kites

G.SRT.5 Use congruence... criteria... to solve problems and to prove relationships in geometric figures.

Goals for this section:

Students should be able to understand what a trapezoid is and its various properties.

Trapezoids

Trapezoid

Trapezoids have one pair of parallel sides called "bases". The other sides are called "legs".

Isosceles Trapezoid

This is a special trapezoid because the legs are congruent, or have the same length.

Isosceles Trapezoid Properties

Each pair of base angles are congruent

So ∠A ≅ ∠B and ∠C ≅ ∠D.

The diagonals are congruent

So AC = BD.

Trapezoid Midsegment Theorem

Recall midsegment. A midsegment connects the midpoint of two opposite sides.

  • The midsegment of a trapezoid is parallel to the bases.
  • The length of the midsegment is half the sum of the length of the bases.

Kites

A kite has two pairs of consecutive sides that are congruent. No opposites sides are congruent.

Kite Diagonal Property

The diagonals of a kite form a 90 degree angle. Notice too that the vertical segment bisects the horizontal segment.

Keywords: trapezoid, kite, perpendicular bisector, parallel lines, midsegment, isosceles, diagonals