Trapezoid = a quadrilateral with exactly one pair of parallel opposite sides.

Bases: the parallel sides

Legs: the non-parallel sides

Theorem 1: Base Angles

In an isosceles trapezoid, the angles adjacent to the same base are equal

∠A = ∠B and ∠D = ∠C

Theorem 2: (Converse)

A trapezoid with equal angles adjacent to the same base is isosceles

Theorem 3: Diagonals

In an isosceles trapezoid, the diagonals are equal

Theorem 4: (Converse)

A trapezoid with equal diagonals is isosceles

Theorem 5: Midsegment

The midsegment of a trapezoid is parallel to the bases and equals half their sum

\(m = \frac{a + b}{2}\)

Theorem 6:

In a trapezoid, a line bisecting one leg and parallel to the bases bisects the other leg

Kite = a quadrilateral with two pairs of equal adjacent sides.

AB = AD and CB = CD

Theorem 7: The Main Diagonal of a Kite

The main diagonal of a kite:

• bisects the apex angles
• bisects the other diagonal
• is perpendicular to the other diagonal

💡 Note:

The main diagonal connects the two apex vertices (where the equal sides meet).