Triangles; Objective: To find the perimeter and area of a triangle.
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Transcript of Triangles; Objective: To find the perimeter and area of a triangle.
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Triangles;Triangles;Objective: To find the Objective: To find the perimeter and area of perimeter and area of
a triangle.a triangle.
Triangles;Triangles;Objective: To find the Objective: To find the perimeter and area of perimeter and area of
a triangle.a triangle.
![Page 2: Triangles; Objective: To find the perimeter and area of a triangle.](https://reader035.fdocuments.net/reader035/viewer/2022062301/56649f2f5503460f94c4969d/html5/thumbnails/2.jpg)
Triangles• A 3-sided figure• named by the three points• endpoints are called vertices of the
triangle
A
B
C
ABC
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3
3
3
534
48
6
Equilateral
RightScalene
Isosceles
44
2All sides equalTwo sides equal
No sides equal Has a 90o angle; special properties
TRIANGLES
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DefinitionNotes about Right Triangles
– The sides of the triangle that create the right angle are called the legs
– The side of the triangle that is opposite the right angle is called the hypotenuse
hypotenuse
leg
leg
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Definition
Notes about Isosceles Triangles– The congruent sides of the triangle
are called the legs– The third side of the triangle is called the base
leg
leg
base
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Equilateral
RightScalene
Isosceles
TRIANGLES
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EXAMPLE #1FIND THE PERIMETER
4 cm
8 cm
6 cm P = 4 + 6 + 8
P = 18 cm
P = s1 + s2 + s3
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The perimeter of the triangle is 16 in.A) What is x?B) What are the side lengths?
2x
x x
16 = 3x - 2
18 = 3x 6 = x
2) 6 in, 6 in, 4 in
EXAMPLE #2
16 = x + x + (x – 2)
A) P = s1 + s2 + s3
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PRACTICE #11. Find the perimeter of the triangle.
6 ft
8 ft10 ft
2. Find the length of the hypotenuse if the perimeter is 12 inches.
X + 1
xX + 2
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Area of a Triangle
• The formula for the area of a triangle is
b = base h = height
h
b
Notice the base and the height form the 90⁰
angle
bhA2
1
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Height/Altitude
hh h
• Height is also called an altitude
• Altitude: a line segment that connects a vertex to the base forming a 90⁰ angle.
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Where does the area formula come from?
Length = Base
Wid
th =
Heig
ht
Area Rectangle = l x w
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Length = Base
Wid
th =
Heig
ht
What shapes do you see?
How much area does one triangle make-up of the rectangle?½
Two triangles
bhA2
1
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8
12
6 9
1
2A b h
112 8
2
6 8
248 units
EXAMPLE #3Find the area of the triangle
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x + 1
x The area of the triangle above is 15 cm2.1)What is the height?2)What is the base?
1
2A b h
230 ( )x x
2 30 0x x
( 6)( 5) 0x x
x = -6
x = 5
Base = 5 cm
Height = 6 cm
EXAMPLE #4
)1)((2
115 xx
)(2
115 2 xx
)(2
115 2 xx
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10 ft 10 ft
6 ft6 ft
What is the area of the unshaded region?
Unshaded region = Area of rectangle – 2( Area of triangle)
= 60 ft2
Area of triangles = 2 (½bh ) = 2(
EXAMPLE #5
Area of rect. = (l x w) = (20)(6) = 120
½)(6)(10) = 60Area of unshaded = 120 – 60
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Pythagorean Theorem
b
a c
• The Pythagorean Theorem is only used with a right triangle.• c represents the hypotenuse.• a and b are the legs of the triangle
222 cba
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x
12 mm
15 mm
Find the area.
EXAMPLE #6
222 1512 x
225144 2 x
812 x
mmx 9
First find the missing side length
A = (9)(12) = 54 mm²½
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PRACTICE #2
1. The length of the base of a triangle is 3 cm and the height is 2 cm. What is the area of the triangle?
2. Find the area of the shaded region.
3.6 in.
4 in.
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http://www.youtube.com/watch?gl=GB&hl=en-GB&v=o2Z6tDSb6c8&feature=related
Triangle song – sesame street