Triangle Inequalities

1
Lesson 4.8

• Triangle Inequalities

2
Investigation

• What would you conclude about the three angles
  given that the three sides are congruent?

CONGRUENT
3
Investigation

• What conclusion would you draw about the angles
  across from the two congruent sides?

A
CONGRUENT
Isosceles Triangle
C
B
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Investigation
A

• Which angle is the smallest?
• Which side is the shortest?

BC
A
C
B
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Isosceles Triangles (SOL Practice 1)

• What is the value of x and y ?

y 70
x 40
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Isosceles Triangles (SOL Practice 2)

• What is the value of x and y ?

x 92
y 7
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Isosceles Triangles (SOL Practice 3)

• What is the value of x and y ?

y 4
x 38
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Triangle Inequality

• The smallest side is across from the smallest
  angle.
• The largest angle is across from the largest side.

BC 3.2 cm
AB 4.3 cm
AC 5.3 cm
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Triangle Inequality examples (SOL Practice 4)
For the triangle, list the angles in order from
least to greatest measure.
4 cm
6 cm
5 cm
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Triangle Inequality examples (SOL Practice 5)
For the triangle, list the sides in order from
shortest to longest measure.
(7x 8) (7x 6 ) (8x 10 )
180 22 x 4 180 22x 176 X 8
mltC 7x 8 64 mltA 7x 6 62 mltB 8x
10 54
54
64
62
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Triangle Inequality Theorem

• The sum of the lengths of any two sides of a
  triangleis greater than the length of the third
  side.

a b gt c a c gt b b c gt a
Example
Determine if it is possible to draw a triangle
with side measures 12, 11, and 17.
12 11 gt 17 ? Yes 11 17 gt 12 ? Yes 12 17 gt
11 ? Yes
Therefore a triangle can be drawn.
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Finding the range of the third side

• Since the third side cannot be larger than the
  other two added together, we find the maximum
  value by adding the two sides.

Since the third side and the smallest side cannot
be larger than the other side, we find the
minimum value by subtracting the two sides.
Example
Given a triangle with sides of length 3 and 8,
find the range of possible values for the third
side.
The maximum value is 3 8
The minimum value is 8 3
5
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Thus the length of the third side is between 5
and 11
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Examples (SOL Practice 6)

• Determine if it is possible to draw a triangle
  with the following side measures
• 3 cm, 4 cm, and 5 cm
• 3 in, 6 in, and 10 in
• 3 cm, 4 cm, and 7 cm
• 20 ft, 15 ft, and 30 ft

YES
NO
NO
YES
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More SOL Practice

• Click on SOL Practice