**Key Terms**

- Base Angles – The two angles formed by the base of a trapezoid and the two adjacent sides.
- Bases – The parallel sides of a trapezoid.
- Isosceles Trapezoid – A trapezoid with two congruent legs.
- The base angles of an isosceles trapezoid are also congruent.

- Legs – The nonparallel sides of a trapezoid.
- Median – The line segment that joins the midpoints of the legs of a trapezoid.
- The median is parallel to the bases, and its length equals the mean of their lengths.

- Trapezoid – A quadrilateral with exactly one pair of parallel sides.

**Review**

- Isosceles
- Two congruent sides
- Congruent base angles

- Consecutive Interior Angles
- Angles between two parallel lines, along the same side (transversal)
- Supplementary (adds up to 180°)
- Adjacent (side by side)

- Diagonals
- Segments that connect opposite vertices.

**Notes**

- Quadrilateral Family Tree and Diagrams

- Diagram of a Trapezoid

- Trapezoid Properties
- A trapezoid is a quadrilateral with exactly one pair of parallel sides.
- Trapezoids are NOT parallelograms
- In a parallelogram,
*both*pairs of opposite sides are parallel. - A trapezoid is
*not*a parallelogram because only one pair of its sides is parallel.

- In a parallelogram,
- Trapezoids are NEVER rectangles, because they can only have ONE pair of parallel sides (not two).
- Trapezoids can have two right angles, but not four.

- Isosceles Trapezoids
- No right angles, not even one.

- Median
- … is a segment that connects the midpoints of the legs of a trapezoid.
- … is always parallel to both bases of a trapezoid.
- … Connects the midpoints of the legs.
- The length of the median is half the sum of the lengths of the bases.

- Median of a Trapezoid Formula

**Examples**

- Ex 1. If TRAP is an isosceles trapezoid, what is the value of x?
- Since and are parallel, and are consecutive interior angles (which are supplementary).
- Setup: 4x + 12 + 2x = 180
- Combine like terms: 6x + 12 = 180
- Subtract 12 on both sides: 6x = 168
- Divide by 6 on both sides: x = 28°

- Ex 2. If SLDG is an isosceles trapezoid, what is the value of x?
- Since the diagonals of an isosceles trapezoid are congruent, they are equal.
- Setup: 8x – 5 = 6x + 21
- Subtract 6x on both sides: 2x – 5 = 21
- Add 5 to both sides: 2x = 26
- Divide both sides by 2: x = 13°

- Ex 3. Given the median and trapezoid MOPN, what is the value of x?
- The formula for finding the median is
- Setup:
- Combine like terms:
- Multiply by 2 on both sides: 11x – 1 = 54
- Add 1 to both sides: 11x = 55
- Divide by 11 on both sides: x = 5

- Ex 4. DEFG is an isosceles trapezoid. Find the measure of .
- Isosceles trapezoids have congruent base angles. So, if then
- Also, and are supplementary (add up to 180°); so, 59 + G = 180. Solve for G.
- Answer: 121°

- Ex 5. Jaime wants to tile his floor using tiles in the shape of a trapezoid.
- To make the pattern a little more interesting he has decided to cut the tiles in half along the median.
- The top base of each tile is 15 inches in length and the bottom base is 21 inches.
- How long of a cut will Jaime need to make so that he cuts the tiles along the median?
- Formula:
- Add the bases:
- What is one-half of 36? Divide 36 by 2 to find out:
- The median = 18 inches