Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 14: Quadrilaterals 187

If the nonparallel sides are congruent, the trapezoid is an isosceles trapezoid. You might have
guessed that you get an isosceles trapezoid by cutting the top off an isosceles triangle, so you
won’t be surprised to hear that the base angles of an isosceles trapezoid are congruent, just as the
base angles of an isosceles triangle are congruent. But you might be surprised to know that the
trapezoid has two sets of base angles: the ones at each end of the longer base and the ones at each
end of the shorter base. The two angles in each set are congruent, and the angles in one set are
supplementary to the angles in the other set.

A trapezoid is a quadrilateral in which one pair of opposite sides are parallel. A trapezoid is an

isosceles trapezoid if the nonparallel sides are the same length.

The line segment joining the midpoints of the nonparallel sides is called the median of the
trapezoid. The median is parallel to the bases. Its length is the average of the bases.

DEFINITION

The median of a trapezoid is a line segment that connects the midpoints of the two

nonparallel sides.

Like all quadrilaterals, a trapezoid has two diagonals. In an isosceles trapezoid, the diagonals
are congruent. Diagonals of other trapezoids are not congruent. Diagonals of a trapezoid do not
bisect one another. That belongs only to parallelograms.

CHECK POINT

11. In trapezoid ABCD, AC BD and MN is a median. AC = 14 cm and BD = 30 cm.
    How long is median MN?


12. In trapezoid FIVE, IV FE and m’F = 59r. What is the measure of ’I?


13. In trapezoid TEAR, EA TR and TE = AR. If ’E = 107r, find the measures of
    ’A and ’R.


14. In trapezoid ZOID, ZDOI. m’Z = 83r and m’I = 97r. If ZO = 4 cm, how long
    is ID?


15. In trapezoid PQRT, PT QR and MN is a median. If MN = 17 inches and PT =
    21 inches, how long is QR?