1. Chapter 5: Quadrilaterals
5-5: Trapezoids

2. Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides.
The parallel sides are called bases.
The other sides are legs.
Notice that the number of parallel sides is “exactly one” and not “at least one.”

3. Median of a trapezoid: the segment connecting the midpoints of the two legs of a trapezoid
only one in each trapezoid
not to be confused with the median of a triangle
is parallel to both bases
equal to the average of the bases A C E B D F

4. Isosceles trapezoid: trapezoid with congruent legs
Base angles are congruent. A B D C

5. A C B D
Prove that the diagonals of an isosceles trapezoid are congruent.
Statements
Reasons
Given
Reflexive Property
Def of isosceles trapezoid
Base of isos trap
SAS ≅
CPCTC

6. 5-5 Trapezoids
The following are trapezoids with their medians shown. Find the value of x. x
7x - 2
3x + 1
2x + 1 9
5x + 3

7. Find the measure of each angle in the isosceles trapezoids.9
3xº xº
130º
Two congruent angles of an isosceles trapezoid have measures (5x – 17)° and (2x + 13)°. Find the value of x.

8. In ∆ABC, AX=XM=MB & AY=YN=NC.
If XY = 9.5, then MN = ___ & BC=___.
If XY = 8 & MN = x+12 then BC=___.

9. B C A D E
Prove: ABCE is a parallelogram.
Statements
Reasons
Given

10. Section 5.5 Written Exercises (p. 192-193) #1-18 (all)
Homework
Section 5.5 Written Exercises (p ) #1-18 (all)
Section 5.4 Written Exercises (p. 188) #28
5.4 Practice Worksheet