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**Pythagorean Relationship 2 (Finding the length of the Hypotenuse)**

Measurement Pythagorean Relationship 2 (Finding the length of the Hypotenuse)

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To review… In a right angle triangle, the side of the triangle opposite the right angle is called the hypotenuse. hypotenuse legs

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**Pythagorean Relationship**

Area = c2 b c Area = b2 c b a a2 + b2 = c2 a Area = a2

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**Applying the Pythagorean Relationship**

We know that: a b2 = c2 a c b

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**Applying the Pythagorean Relationship**

Using this… If we know the lengths of ANY two sides of a right angle triangle, we can use the Pythagorean Relationship to find the length of the unknown side. a c b

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**Applying the Pythagorean Relationship**

Situation One: We know the lengths of the two legs (a and b) of a right triangle. How can we find the length of the hypotenuse (c)? a c b

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**Applying the Pythagorean Relationship**

Since we know that: a2 + b2 = c2 Then: c2 = a2 + b2 a c b

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**Applying the Pythagorean Relationship**

Since: c2 = a2 + b2 Then: c = (a2 + b2) a c b

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**Applying the Pythagorean Relationship**

Example: a = 7m; b = 5m c = (a2 + b2) c = ( ) c = ( ) c = c = m a = 7m c = ? b = 5m

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Problem a = 3cm Find the length of the hypotenuse, “c”. b = 6cm c = ?

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Pythagorean Theorem & its Converse 8 th Grade Math Standards M.8.G.6- Explain a proof of the Pythagorean Theorem and its converse. M.8.G.7 - Apply the.

Pythagorean Theorem & its Converse 8 th Grade Math Standards M.8.G.6- Explain a proof of the Pythagorean Theorem and its converse. M.8.G.7 - Apply the.

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