Theorems involving Trapezoids

In these lessons, we will learn how to use theorems involving trapezoids in High School Math as required for the Regents Exam math conducted by NYSED.

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The following diagram shows some theorems for rectangles, rhombuses, and squares. Scroll down the page for more examples and solutions on postulates and theorems for rectangles, rhombuses, and squares.

Theorem Trapezoid

Trapezoid and Kite Theorems & Corollaries


  1. Midsegment Theorem for Trapezoids
    The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases (average of the bases)

  2. If a trapezoid is isosceles, then each pair of base angles is congruent.

  3. If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

  4. A trapezoid is isosceles if and only if its diagonals are congruent.

  5. If a quadrilateral is a kite, then its diagonals are perpendicular.

  6. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

Isosceles Trapezoid Theorem

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