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?

Right Triangles in Algebra Chapter 11 Right Triangles in Algebra

11.2 – The Pythagorean Theorem (Page 592) Essential Question: How can we prove that a triangle is a right triangle?

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

11.2 cont. Pythagorean Theorem: ?

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

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

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

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

11.2 cont. Video Clip

11.2 - Closure How can we prove that a triangle is a right triangle? USE THE PYTHAGOREAN THEOREM!!

11.2 - Homework P 595-596; 2-28 even