This document discusses properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one pair of parallel opposite sides. An isosceles trapezoid is a trapezoid where the two non-parallel sides, or legs, are congruent. The document includes examples of identifying trapezoids and isosceles trapezoids based on side lengths and slopes. It also defines the median of a trapezoid as the segment joining the midpoints of the legs. Theorems and examples are provided about angles and properties of trapezoids. Review and practice questions are listed at the end.
5. Example 1: Identify Trapezoids
Quadrilateral QRST has vertices Q(-3, 2), R(-1, 6),
S(4, 6), and T(6, 2).
a. Verify that QRST is a trapezoid.
A quadrilateral is a trapezoid if exactly one pair of
opposite sides is parallel
Use the Slope Formula.
Exactly one pair of opposite sides
parallel. So, QRST is a trapezoid.
6. b. Determine whether QRST is an
isosceles trapezoid. Explain.
First use the Distance Formula to show
that the legs are congruent.
Since the legs are congruent, QRST is an isosceles
trapezoid.
7. Medians of Trapezoids The segment that
joins the midpoints of the legs of a
trapezoid is called the median
12. Question 3 on page 358
Questions 4A and 4B on page 359
Questions 5-6, 18, 20, 21-22,
and 25-26 on pages 359-369
Extra challenge
Questions 1 and 7-10
