Lesson 5-5: Inequalities in Triangles

1
Lesson 5-5 Inequalities in Triangles
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Angle-Side Relationship

• Think of two flashlights shining on a wall

The flashlight with the widest opening makes a
longer segment on the opposite wall,
similarly
? The widest angle has the longest side opposite
to it.
? The narrowest angle has the shortest side
opposite to it.
3
Write the measurements of the triangles in order
from least to greatest.
SOLUTION
SOLUTION
JH
lt GH
lt JG
m? R
lt m? P
lt m?Q
4
Can you make a triangle with any 3 sides?

• Draw a triangle with sides 3, 6, and 8 inches
• Draw a triangle with sides 3, 6, and 9 inches
• Draw a triangle with sides 3, 6, and 10 inches.

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3 Sides Inequality

• Any 2 sides must be greater than the 3rd side
• Testing 3 sides
• 2 smaller sides must be more than 3rd side
• Range for 3rd side
• Order sides
• Subtract left, add right
• 3rd side must be between (not equal! )

6

• Can 13, 21, 33 be the sides of a triangle?
• Given 12 cm and 15 cm, what are the possibilities
  for the 3rd side?

Two smaller sides 13 21 ?
34 ? bigger than 3rd side ? YES
Order, subtract left, add right
15 12 3 12 15 27
3rd side must be between 3 and 27 ? 3 lt 3rd side
lt 27