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Bell Ringer Get out your 10.5/10.7 homework assignment and formula sheet Get out your notebook and prepare to take notes on Section 11.2 What do you know about the following right triangle?

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**Right Triangles in Algebra**

Chapter 11 Right Triangles in Algebra

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**11.2 – The Pythagorean Theorem (Page 592)**

Essential Question: How can we prove that a triangle is a right triangle?

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11.2 cont. Right Triangles: Hypotenuse – longest side, opposite the right angle

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11.2 cont. Pythagorean Theorem: ?

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11.2 cont. Example 1: Find c, the length of the hypotenuse, in the following triangle: 𝒂 𝟐 + 𝒃 𝟐 = 𝒄 𝟐 𝟔 𝟐 + 𝟖 𝟐 = 𝒄 𝟐 𝟑𝟔+𝟔𝟒= 𝒄 𝟐 𝟏𝟎𝟎= 𝒄 𝟐 𝟏𝟎𝟎 =𝒄 𝟏𝟎=𝒄

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11.2 cont. Example 2: In a given right triangle, the hypotenuse is 9 in and one of the legs is 6 in. Find the missing leg of the triangle. 𝒂 𝟐 + 𝒃 𝟐 = 𝒄 𝟐 𝟔 𝟐 + 𝒙 𝟐 = 𝟗 𝟐 𝟑𝟔+ 𝒙 𝟐 =𝟖𝟏 𝒙 𝟐 =𝟒𝟓 𝒙= 𝟒𝟓 𝒙≈𝟔.𝟕

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11.2 cont. Example 3: Find the height of the following isosceles triangle: 𝒂 𝟐 + 𝒃 𝟐 = 𝒄 𝟐 𝒉 𝟐 + .𝟕𝟓 𝟐 = 𝟏.𝟓 𝟐 𝒉 𝟐 +.𝟓𝟔𝟐𝟓=𝟐.𝟐𝟓 𝒉 𝟐 =𝟏.𝟔𝟖𝟕𝟓 𝒉= 𝟏.𝟔𝟖𝟕𝟓 𝒙≈𝟏.𝟑 h

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11.2 cont. Example 4: Is a triangle with sides 12 m, 15 m, and 20 m a right triangle?

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11.2 cont. Video Clip

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**11.2 - Closure How can we prove that a triangle is a right triangle?**

USE THE PYTHAGOREAN THEOREM!!

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Homework P ; 2-28 even

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