U4 L4 Trapezoids.notebook
January 26, 2017
U4 L4 Trapezoids DO NOW!
Suppose the diagonals of a parallelogram are both perpendicular and congruent . What type of special quadrilateral is it? Explain your reasoning.
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U4 L4 Trapezoids.notebook
January 26, 2017
Common Core Definition
A Quadrilateral with @ least one pair of parallel sides.
The old way... By definition , A Trapezoid is a quadrilateral with exactly one pair of parallel sides.
Trapezoid
base
The parallel sides are known as the BASES...
leg
leg
It has 2 pairs of base angles
The Non­Parallel sides are called the LEGS
base
What is an Isosceles Trapezoid?
An Isosceles Trapezoid is a trapezoid with congruent legs
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U4 L4 Trapezoids.notebook
January 26, 2017
Given isosceles trapezoid ABCD, if the m<A = 60 degrees, find the remaining angles.
D
A
C
B
Theorems involving Trapezoids
If a Trapezoid is ISOSCELES, then each pair of base angles are congruent
The converse is also true!
If a Trapezoid has a pair of congruent base angles, then it is an ISOSCELES Trapezoid
Also, consecutive angles that are NOT base angles are supplementary.
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U4 L4 Trapezoids.notebook
January 26, 2017
Examples:
Find the angle measures of ABCD
1.
<
D
<
A
A
2.
D
C
132o
B
<
<
B
76o
C
Another Trapezoid Theorem A Trapezoid is ISOSCELES if and only if the diagonals are congruent
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U4 L4 Trapezoids.notebook
January 26, 2017
Prove the theorem that states that the diagonals of an isosceles trapezoid are congurent:
Statements
Reasons
1) given
Recall a midsegment for triangles.....
The midsegment for a trapezoid is parallel to each base and is one­half the sum of the bases.
50
T
R
N
M
H
W
70
Find the length of the midsegment.
example: A potter crafts a trapezoidal relish dish, placing a divider, shown by AB, in the middle of the dish. How long must the divider be to ensure that it A
divides the legs in half?
Find the value of x, knowing that the picture contains a trapezoid with its midsegment.
24
13
8
B
12
x
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U4 L4 Trapezoids.notebook
January 26, 2017
Quick and easy Proof:
D
E
given:
F
prove: DAVE is an Isosceles Trapezoid
A
Statements
1.
V
Reasons
1. Given
Homework
U4 L4 Trapezoid HW Online
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U4 L4 Trapezoids.notebook
January 26, 2017
U4 L4 More Trapezoids
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U4 L4 Trapezoids.notebook
January 26, 2017
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U4 L4 Trapezoids.notebook
January 26, 2017
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U4 L4 Trapezoids.notebook
January 26, 2017
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