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Unit 22
TRIANGLES
TYPES OF TRIANGLES




A polygon is a closed plane figure
formed by three or more line segments
A triangle is a three-sided polygon
The sum of the angles of any triangle
is equal to 180°
An equilateral triangle has three equal
sides. It also has three equal angles
2
TYPES OF TRIANGLES

An isosceles triangle has two equal
sides.




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The equal sides are called legs.
The third side is called the base.
The base angles of an isosceles triangle
are equal
The base angles are opposite the legs
A scalene triangle has three unequal
sides.

It has three unequal angles.
3
TYPES OF TRIANGLES
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

A right triangle has a 90° angle. The
symbol for a right angle is a small
square placed at the vertex of the
angle. The side opposite the right
angle is called the hypotenuse. The
other two sides are called legs
An acute triangle has three acute
angles
An obtuse triangle has one obtuse
angle and two acute angles
4
ISOSCELES AND EQUILATERAL
TRIANGLES
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

In an isosceles triangle, an altitude to
the base bisects (divides into two equal
parts) the base and the vertex angle
In an equilateral triangle, an altitude to
any side bisects the side and the
vertex angle
Find sides c and b in the figure below:
25"
c
50°
50°
13"
b
• c = 25" (isosceles triangle)
• b = 26" (13" × 2)
5
PYTHAGOREAN THEOREM


The Pythagorean Theorem deals with
the relationship of the sides of a right
triangle
The Pythagorean Theorem states that
in a right triangle, the square of the
length of the hypotenuse is equal to
the sum of the squares of the lengths
of the legs
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PYTHAGOREAN THEOREM

Determine the hypotenuse (c) in the
right triangle below:
c
5"
7"
c 2 = 5 2 + 72
c2 = 25 + 49
c2 = 74
c = 8.60 Ans
Note: The answer is rounded
7
PRACTICE PROBLEMS

1.
Identify the triangles in problems 1–
3 as scalene, isosceles, or
equilateral
4"
4"
2. 5mm
20mm
17mm
4"
3.
20"
15"
15"
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PRACTICE PROBLEMS
(Cont)

Define the terms in problems 4–6:
4.
5.
6.
7.
8.
Obtuse triangle
Right triangle
Polygon
Given a triangle with 1 = 25, 2 = 68,
find 3.
Find A and B in the triangle below
C
given that C = 30°. 5"
5"
A
B
9
PRACTICE PROBLEMS
(Cont)
9.
Determine side a in the right triangle
shown below.
3.5"
a
2"
10.
Use the Pythagorean Theorem to find
the length of the diagonal in a
rectangle with a length of 10 inches
and a width of 8 inches.
10
PRACTICE PROBLEMS (Cont)
11.
12.
If you know the roof on your house is
40 feet from eve to vertex (peak) and
that the width is about 55 feet. How
tall is the peak on your house from the
ceiling?
In the house above if the peak is 86°
15‘48“. What is the angle of the roof to
ceiling/trusses on the right side in
DMS?
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PROBLEM ANSWER KEY
Equilateral
2. Scalene
3. Isosceles
4. Has one obtuse angle and two acute angles
5. Has a right or 90° angle
6. A closed plane figure formed by three or more
line segments
7. 87°
8. A = B = 75
9. 2.872 inches (rounded)
10. 12.806 inches (rounded)
11. 29.047 feet
1.
12.
46°52‘6“
12