Areas of Parallelograms and Triangles
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Transcript of Areas of Parallelograms and Triangles
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Areas of Parallelograms and Triangles
Lesson 7-1
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Thm 7-1 Area of a Rectangle
For a rectangle, A=bh.(Area = base · height)
h
b
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AREA OF A PARALLELOGRAM
To do this let’s cut the left triangle and…
h
b
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slide it…
h
h b
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slide it…
h
h
b
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slide it…
h
h
b
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slide it…
h
hb
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…thus, changing it to a rectangle.
What is the area of the rectangle?
h
b
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Thm 7-2Area of a Parallelogram
For a parallelogram, A=bh.
h
b
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Parts of a Parallelogram
Base – any side of the parallelogram. Altitiude – the perpendicular segment
form the line containing one base to the opposite base.
Height – length of the altitude.
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Finding the Area of a Parallelogram
Find the area of the parallelogram.
A = 96m2
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Finding a Missing Dimension
For parallelogram ABCD, find CF to the nearest tenth.
10 in.
12 in.13 in.
A BE
CD
F
X1st: Find area of ABCD
a = b ha = 10 (12) = 120 in2
2nd: Use area formula for other base and height
a = b h120 = 13 (x)x 9.2
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Thm 7-3Area of a Triangle
For a triangle, A= ½ bh.
h
b
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Finding the Area of a Triangle
Find the area of XYZ.
A = 195 cm2
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Find the area of parallelogram PQRS with vertices P(1, 2), Q(6, 2), R(8, 5), and S(3, 5).
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The Pythagorean Theorem and Its Converse
Lesson 7-2
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Pythagorean Thm
If a triangle is right, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a2 + b2 = c2
b
a
c
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GSP
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How high up on the wall will a twenty-foot ladder reach if the foot of the ladder is placed five feet from the wall?
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Pythagorean Triples Any set of three whole numbers that satisfy the
Pyth. Thm. are called a Pythagorean Triple. Which of the following are?
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Using the Pythagorean Thm.
A right triangle has legs of length 16 and 30. Find the length of the hypotenuse. Do the lengths of the sides form a Pythagorean triple?
34. Yes.
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summary
So, if a2 + b2 = c2 and a, b, & c are integers, then a, b, & c form a pythagorean triple
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Properties of Exponents
Multiplication Multiplication Property of Property of ExponentsExponents
Power Power Properties of Properties of ExponentsExponents
Division Division Property of Property of ExponentsExponents
bm·bn = bm+n(bm)n = bmn
(ab)n = anbn
mnm
nb
b
b
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Express each square root in its simplest form by factoring out a perfect square.
12 18 24 32 40
48 60 75 83 85
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Express each product in its simplest form.
223
234
232
3263237
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More practice simplifying expressions
1. 2.
3. 4.
369 3250
7218 238
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example
Find the value of x. Leave your answer in simplest radical form.
112x
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Example 4: SAT
In figure shown, what is the length of RS?
7
3
RT
S
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Finding Area
The hypotenuse of an isosceles right triangle has length 20 cm. Find the area.
1002102102
12
1
210
A
bhA
x
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Real World Connection
A baseball diamond is a square with 90-ft sides. Home plate and second base are at opposite vertices of the square. About how far is home plate from second base?
Stinks!!!Boooo…
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Converse of the Pythagorean Thm.
If the square of the length of one side of a triangle is equal to the sum of the lengths of the other two sides, then it is a right triangle.
GSP
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Example
Which of the following is a right triangle?
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Acute Triangle TheoremAcute Triangle Theorem
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then it is an acute triangle.
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Obtuse Triangle TheoremObtuse Triangle Theorem
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then it is an obtuse triangle.
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Classifying
The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse, or right.
a. 15, 20, 25 b. 10, 15, 20
Right Obtuse
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Example 5
Can segments with lengths 4.3 feet, 5.2 feet, and 6.1 feet form a triangle? If so, would the triangle be acute, right, or obtuse?
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Assignment
Pg. 3602-44 even, 48-51, 76-77
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Classwork/Homework
Pg. 3511,3, 9-23 odd, 26, 30-32, 44-46, 49
Pg. 3601-43 odd, 44, 48-53, 76-77