Chapter 5: Quadrilaterals 5-5: Trapezoids

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.”

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

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

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

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

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.

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

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

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