Trapezoids

April 29, 2008

What is a trapezoid?

• A quadrilateral with exactly one pair of parallel sides is called a trapezoid. The parallel sides are called the bases and the other sides are called the legs.

More about trapezoids

• Notice that we can prove that exactly one pair of opposite sides of the quadrilateral above are parallel.

• We have two lines cut by a transversal so that same side interior angles are supplementary.

• The bases are the two parallel sides, not top and bottom.

Isosceles Trapezoids

• A trapezoid with congruent legs is called an isosceles trapezoid.

• If you cut out an isosceles trapezoid from a piece of paper and fold it over so that the legs coincide, you will find the both pair of base angles are congruent.

Theorem: The base angles of an isosceles trapezoid are congruent.

• How would you show that angle A and angle B are congruent?

Diagonals of an isosceles trapezoid

• What do you notice about the diagonals of the isosceles trapezoid?

Median of a Trapezoid

• The median of a trapezoid is the segment that joins the midpoints of the legs.

• The median of a trapezoid is very similar to the midsegment of a triangle in that both join the midpoints of sides.

Theorem: The median of a trapezoid

The median of a trapezoid…• is parallel to the bases;• has a length equal to the average of the

base lengths (i.e. 1/2 the sum of the lengths of the bases)

Using the median of trapezoid

• What would you do to find x?

Finding angle measures in an isosceles trapezoid

• Two congruent angles of an isosceles trapezoid have measures 3x + 10 and 5x -10. Find the value of x and then give the measures of all angles of the trapezoid.

Summary

• In summary, a trapezoid is a special quadrilateral in which exactly one pair of opposite sides is parallel.

• This, of course, means that a trapezoid is never a parallelogram since a parallelogram must have both pairs of opposite sides parallel.

• An isosclele trapezoid is a trapezoid in which the legs are congruent ( which in turn means that the base angle and the diagonals are also congruent.).