Pythagorean inequalities assist in determining whether a triangle is a right acute or obtuse triangle.

Pythagorean Inequalities:

In ΔABC  “c” is the length of the longest side.

If a2 + b2 > c2, then ΔABC  is an acute triangle

If a2 + b2 < c2, then  ΔABC  is an obtuse triangle

The Pythagorean Theorem always works for right triangles. It is also used to classify triangles that are not right triangles.

Example: Let a = the smallest side
Let b = the middle length side
Let c = the longest side

#### Fill in the Blanks

• The Pythagorean Theorem is ______?______
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a2 + b2 = c2
• The shortest side "a" is: __?___
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7 cm
• The middle side "b"  is: ___?___
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8 cm
• Square "a" and "b"  and add them together: ____?____
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49 + 64 = 113
• The longest side "c" is: ___?____
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9 cm
• Square "c": ___?____
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92 = 81
• a2 + b2_?__c2 ?
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>
• When a2 + b2 > c2 the triangle is an ___?___ triangle.
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acute

#### Triangle 2 – An Obtuse Triangle

• The Pythagorean Theorem is ____?______
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a2 + b2 = c2
• The shortest side "a" is _____?_____
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16 cm
• The middle side "b" is ____?______
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19 cm
• Square "a" and "b" and add them together. ____?_____
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256 + 361 = 617
• The longest side "c" is: ____?_____
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25 cm
• Square "c": _____?____
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252 = 625
• a2 + b2 _?_ c2 ?
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<
• When a2 + b2 = c2 the triangle is an ____?_____ triangle.
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obtuse

If a2 + b2 < c2,
then the triangle is an ____?_____ triangle. Interactive popup. Assistance may be required.

obtuse

If a2 + b2 > c2,
then the triangle is an ____?____ triangle.
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acute

#### You try it!

The measurements of 3 sides of a triangle are given. Identify the following as a right triangle, acute triangle, or obtuse triangle.

The measurements of 3 sides of a triangle:

1. 5, 12, 13 ___?____
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Right Triangle
2. 7, 8, 9    ____?____
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Acute Triangle
3. 6, 8, 10    ___?____
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Right Triangle
4. 13, 15, 21   __?___
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Obtuse Triangle
5. 7, 10, 12    ___?___
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Acute Triangle