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GEOMETRY
LESSON 8-6
Pg 439-445
TRAPEZOIDS
Objectives:
- Recognize and apply the proper properties of a trapezoid, then solve problems dealing with the medians
of trapezoids to find missing elements
- Understand the relationship of medians to the bases and angle relationships of trapezoids
Key Concept: A trapezoid is a quadrilateral (four-sided figure) with exactly one pair of parallel sides called
bases, and two connecting sides called legs. (Looks like a triangle with the top cut off)
If both legs are congruent, it is a special case called an “Isosceles Trapezoid”
Keys to Remember about the Trapezoid:
1) If we connect the MIDPOINTS of both the legs, it forms a Median (Midsegment)
a. This median is ALWAYS parallel to both bases.
b. The MEDIAN measure is exactly ½ the sum of the two bases (THEOREM 8:20)
2) All four angles add to 360 degrees, but no other immediate relationship exist.
3) With an Isosceles Trapezoid, the base angles are congruent (top with top and bottom with bottom)
a. therefore the sum of a bottom and top angle combination will be supplementary
b. Isosceles Trapezoid diagonals will cut each other proportionally to each other
i.Top segment equal the top segment of the other diagonal
ii.Bottom segment equal to the bottom segment of other diagonal
iii.Both diagonals will be cut at a ratio equal to the ratio of the two parallel bases
4) The Area of a Trapezoid
a. The area of a trapezoid requires the “altitude” measure in the formula. The altitude is the
perpendicular segment to both bases with endpoints resting on the each of the parallel bases
b. The formula is Area equals half the sum of the length of the bases multiplied by its altitude
A = 1/2 (b1 + b2)(alt)
** Half the sum of the two bases also is the measure of the “median” so A = (median)(altitude)
Base #1 (b1)
Altitude
Base #2 (b2)
SAMPLE PROBLEMS: #7. EFGH is an isosceles trapezoid with median YZ
EF = 3x + 8
HG = 4x – 10 YZ = 13
Find “x”
H
4x – 10
G
E
3x + 8
F
#14. For trapezoid RSTV, A and B are midpoints of the legs. Find VT given the info in the diagram
#16. For trapezoid QRST, A and B are midpoints of the legs; Find AB, m angle Q and m angle S given
the data on the diagram.