warm up 1. find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. find the area of...
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![Page 1: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/1.jpg)
Warm Up
1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft.
3. Find the area of a parallelogram with height 9 in. and base length 15 in.
2. Find the area of a rectangle with side lengths 24 in. and 32 in.
64 ft
768 in2
135 in2
Pre-Algebra
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2
Pre-Algebra
Exploring
Triangles
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3
Naming Triangles
For example, we can call the following triangle:
Triangles are named by using its vertices.
∆ABC ∆BAC
∆CAB ∆CBA∆BCA
∆ACB
A
B
C
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4
Opposite Sides and Angles
A
B C
Opposite Sides:
Side opposite to A :
Side opposite to B :
Side opposite to C :
Opposite Angles:
Angle opposite to : A
Angle opposite to : B
Angle opposite to : C
BC
AC
AB
BC
AC
AB
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5
Classifying Triangles by Sides
Equilateral:
Scalene: A triangle in which all 3 sides are different lengths.
Isosceles: A triangle in which at least 2 sides are equal.
A triangle in which all 3 sides are equal.
AB
= 3
.02
cm
AC
= 3.15 cm
BC = 3.55 cm
A
B CAB =
3.47
cmAC = 3.47 cm
BC = 5.16 cmBC
A
HI = 3.70 cm
G
H I
GH = 3.70 cm
GI = 3.70 cm
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6
Classifying Triangles by Angles
Acute:
Obtuse:
A triangle in which all 3 angles are less than 90˚.
A triangle in which one and only one angle is greater than 90˚& less than 180˚
108°
44°
28°B
C
A
57 ° 47°
76°
G
H I
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7
Classifying Triangles by Angles
Right:
Equiangular:
A triangle in which one and only one angle is 90˚
A triangle in which all 3 angles are the same measure.
34
56
90B C
A
60
6060C
B
A
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8
polygons
Classification by Sides with Flow Charts & Venn Diagrams
triangles
Scalene
Equilateral
Isosceles
Triangle
Polygon
scalene
isosceles
equilateral
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9
polygons
Classification by Angles with Flow Charts & Venn Diagrams
triangles
Right
Equiangular
Acute
Triangle
Polygon
right
acute
equiangular
Obtuse
obtuse
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10
Theorems & Corollaries
The sum of the interior angles in a triangle is 180˚.
Triangle Sum Theorem:
Third Angle Theorem:
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
Corollary 1: Each angle in an equiangular triangle is 60˚.
Corollary 2: Acute angles in a right triangle are complementary.
Corollary 3: There can be at most one right or obtuse angle in a triangle.
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Example 1: Finding the Perimeter of Triangles
A. 4
10= 21 units
7
P = 4 + 7 + 10
Add all sides.
Find the perimeter of each figure.
B.6
11
P = 9 + 6 + 119
= 26 units
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A triangle can be thought of as half of a parallelogram.
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Triangle: The area A of a triangle is one-half the base length b times the height h.
AREA OF A TRIANGLEWords Numbers Formula
A = (8)(4) = 16 units2
1 2
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A. (–2, 2), (4, 2), (0, 5)
x
y
6
3
= 9 units2
A = bh12
Additional Example 2A: Finding the Area of Triangles Graph and find the area of the figure with the given vertices.
(4, 2)
(0, 5)
(–2, 2)= • 6 • 31
2
Area of a triangle
Substitute for b and h.
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A. (–1, 1), (1, 7), (7, 1)
Try This: Example 2A
Graph and find the area of the figure with the given vertices.
x
y
8
(1, 7)
(–1, 1) (7, 1)= 24 units2
A = bh12
= • 8 • 612
Area of a triangle
Substitute for b and h.6
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Classifying Triangles
by sides and angles
Beat the Computer Drill
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Directions:When the slide appears, say BOTH NAMES for the type of triangle aloud before the computer shows you the
answer. Classify each triangle by both its SIDES and its ANGLES. You will have 6
seconds.
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Classify by sides:
Classify by angles:
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Classify by sides:
Classify by angles:
alsoIsosceles Triangle
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Classify by sides:
Classify by angles:
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Classify by sides:
Classify by angles:
![Page 22: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/22.jpg)
Classify by sides:
Classify by angles:
![Page 23: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/23.jpg)
Classify by sides:
Classify by angles:
![Page 24: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/24.jpg)
Classify by sides:
Classify by angles:
![Page 25: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/25.jpg)
Classify by sides:
Classify by angles:
![Page 26: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/26.jpg)
Classify by sides:
Classify by angles:
![Page 27: Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. Find the area of a parallelogram with height 9 in. and base length](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d845503460f94a6aea9/html5/thumbnails/27.jpg)
Classify by sides:
Classify by angles: