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3.12 Trapezoid

  • Is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases
  • A trapezoid has two pairs of base angles. For example in the trapezoid ABCD,

    A and B are one pair of base angles, and C and D are the second pair.
  • The non parallel sides are the legs of the trapezoid.
Isosceles Trapezoid: If the legs of the trapezoid are congruent then the trapezoid is an Isosceles trapezoid.

  • If a trapezoid is isosceles, then each pair of base angles is congruent.
    If trapezoid ABCD is isosceles, then A @ D and B @ C.
  • If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid ABCD is isosceles. If A @ D and B @ C. then ABCD is isosceles.

  • A trapezoid is isosceles if and only if its diagonals are congruent.
    Trapezoid ABCD is isosceles if and only if AC @ BD.

  • 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. If MN is the midsegment of trapezoid ABCD, then MN // AB, MN // DC, and MN = 1/2(AB+CD)

1) For the trapezoid ABCD shown below find the measures of angle A, angle C and angle D.

2) Answer the following questions and write at least 5 examples of your own.

Q 1: ABCD is a trapezoid. Using the mid segment theorem find the value of x.


Q 2: A trapezoid is a quadrilateral with exactly ___ pair of parallel sides.

Q 3: ABCD is a trapezoid. Measure of angle B is 1180. Find the measure of angle A.


Q 4: A trapezoid has two pairs of _____ angles.

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!

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