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Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
Objectives: By the end of this lesson, you will be able to…
 Recognize the properties of trapezoids.
 Use the properties of trapezoids in proofs and other problems.
Key Definitions:
base
Trapezoid: A quadrilateral with exactly one pair of parallel sides.
The parallel sides are called bases.
leg
leg
The non parallel sides are called legs.
Base angles are the two consecutive angles whose common side is a base.
Name the pairs of base angles and the common base they share.
base
A trapezoid is an Isosceles Trapezoid if its legs are ________________________
Theorem #1: Both pairs of base angles of an isosceles trapezoid are _________________________
What about ∠𝐴 𝑎𝑛𝑑 ∠𝐵? They are _____________________, as are ∠𝐶 𝑎𝑛𝑑 ∠𝐷.
Example 1: An isosceles trapezoid LAKE has A = 76. Find the measures of the other
3 angles.
Example 2: Find the perimeter of isosceles trapezoid ABCD if the bases AB and CD are
12 and 22 respectively and the height is 12.
A
D
B
C
Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
Given: Trapezoid NYPD with vertices N(2, -9), Y(-1, 1), P(3, 8), D(10, 5).
Step 1: Graph the trapezoid and find the slopes of all four sides.
mNY
mYP
mPD
mND
Which pair of sides are the bases? Why?
Step 2: Determine the lengths of bases.
Are the bases congruent?
Step 3: Determine the coordinates for the midpoints of both legs, plot them, and then
connect them with a segment. This is called the median. Label the endpoints of the
median, A and B.
Step 4: Find the slope of median AB
Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
What do you notice about the slope of AB and the other sides of the trapezoid?
Step 5: Find the length of median AB
Step 6: Calculate YP + ND.
What conclusion can you make about sum of the measures of the bases (YP + ND) and
the length of the median?
This gives us our last theorem…
Theorem 3: The median of a trapezoid is parallel to the bases and its measure is
__________________ the sum of the measures of the bases.
Example 3: Given trapezoid TRIP, with median EF, find the value of x.
Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
Example 4: ABCD is an isosceles trapezoid with bases AD and BC. Use the figure and
the given information to solve each problem.
a) If BA = 9, find CD
b)If AC = 21, find BD
b) If AC = 4y – 5, and BD = 2y + 3, find AC and BD.
c) If mBAD  123, find mCBA
d)If mADC  105, find mDAB
Example 5: Find the length of the median of a trapezoid with vertices at (1, 0), (3, -1), (6,
2), and (7, 6).
Practice
1) Given trapezoid TRAP with median EZ,
a) Find EZ if TR = 42 and PA = 30
b) Find TR if EZ = 17 and PA = 14
Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
2) In isosceles trapezoid SNAP with median
OH, find all the missing angle measures:
m∠1 = ______
m∠2 = ______
m∠3 = ______
m∠4 = ______
m∠5 = ______
m∠6 = ______
m∠7 = ______
3) If possible, draw a trapezoid that has the following characteristics. If the trapezoid
cannot be drawn, explain why.
a) Three congruent sides
b) Congruent bases
c) a leg longer than both bases
d) bisecting diagonals
e) Two right angles
f) four acute angles
g) One pair of opposite angles congruent
4) Given trapezoid GHIJ with median KL, find the value of x
Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
5) Given 𝑚∠𝐸 = (2𝑦 2 − 25)° and 𝑚∠𝐻 = (𝑦 2 + 24)° find the value of y so that EFGH
is isosceles.
6)
Find the measure of each angle.
7) PQRS is an isosceles trapezoid with bases PS and QR. Use the figure and the given
information to solve each problem.
a. If PS = 20 and QR = 14, find TV
b. If QR = 14.3, and TV = 23.2, find PS
c. If TV = x + 7, and PS + QR = 5x + 2, find x.
d. If mRVT  57 , find mQTV .
Geometry 300
6.6-Trapezoids
Name_________________________
Chapter 6 Day 7
8) In the accompanying figure, isosceles trapezoid ABCD has bases of length 5 and 11
and an altitude of length 4. Find AB.
5
B
C
4
A
11
D
10) Show that QRST is a trapezoid if Q(-1,-2), R(6,-2), S (10,1), T (7,4).
a. What are the coordinates of the median of QRST?
b. Prove that the median of the trapezoid is parallel to the bases
c. Prove that the median has a length equal to the average of the base
lengths.