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Transcript
```15-2: Trapezoids
Objectives:
1. To discover and use
properties of
trapezoids
2. To find the area of
trapezoids
Assignment:
SpringBoard:
• P: 212: 11, 12
• P. 221: 2-4
Purple Geometry Text:
• P. 546-9: 6-9, 32, 37-39
• P.733-6: 5, 16, 17, 19, 26,
29
• Almost a Trapezoid
Worksheet
You will be able to
discover and use
properties of trapezoids
Objective 1
Trapezoids
What makes a quadrilateral a trapezoid?
Trapezoids
A trapezoid is
with exactly
one pair of
parallel
opposite sides.
Trapezoid Parts
The parallel sides are
called bases
The non-parallel
sides are called legs
A trapezoid has two
pairs of base angles
Example 1
Find the value of x.
C
B
100
x
A
D
Trapezoid Theorem 1
If a quadrilateral is a trapezoid, then the
consecutive angles between the bases are
supplementary.
C
B
y
x
A
t
r
D
If ABCD is a trapezoid, then x + y = 180° and r + t = 180°.
Midsegment
A midsegment of a
trapezoid is a
segment that
connects the
midpoints of the
legs of a
trapezoids.
Investigation 1
In this Investigation, you
will be using
to construct an
isosceles trapezoid,
and then you will
discover some
base angles, diagonals,
and midsegment.
Trapezoid Midsegment Theorem
The midsegment of a
trapezoid is parallel
to each base and its
length is one half
the sum of the
lengths of the
bases.
If
Example 2
Find the value of x.
Example 3
Given: Trapezoid 𝐸𝐹𝐺𝐻
𝑀𝑁 is a midsegment
Prove: 𝑀𝑁 ∥ 𝐹𝐺 and 𝑀𝑁 ∥ 𝐸𝐻
𝑀𝑁 =
1
2
𝐹𝐺 + 𝐸𝐻
Isosceles Trapezoid
An isosceles trapezoid is a
trapezoid with congruent legs.
Trapezoid Theorem 2
If a trapezoid is isosceles, then each pair of
base angles is congruent.
Trapezoid Theorem 3
A trapezoid is isosceles if and only if its
diagonals are congruent.
T
i
Example 4
Find the measure of each missing angle.
Example 5
Given: Trapezoid 𝐶𝑂𝑅𝐸
𝐶𝑂 ≅ 𝐸𝑅
Prove: 𝐶𝑅 ≅ 𝐸𝑂
Objective 2
You will be able to find the area of trapezoids
Investigation 2
Now you will discover
a justification for
the area formula for
trapezoids.
Trapezoid Area
Example 6
Find the area of the polygon.
Example 7
Find the area of the trapezoid.
15-2: Trapezoids
Objectives:
1. To discover and use
properties of
trapezoids
2. To find the area of
trapezoids
Assignment:
SpringBoard:
• P: 212: 11, 12
• P. 221: 2-4
Purple Geometry Text:
• P. 546-9: 6-9, 32, 37-39
• P.733-6: 5, 16, 17, 19, 26,
29
• Almost a Trapezoid
Worksheet
```
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