7.1 Apply the Pythagorean Theorem

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Presentation transcript:

7.1 Apply the Pythagorean Theorem Before: You learned about relationships within triangles Now: You will find side lengths in right triangles. Why?: So you can find the shortest distance between objects.

Pythagorean Theorem Basics In a right triangle, the sum of the squares of the measures of the legs equals the square of the hypotenuse. Legs: the two shorter sides, either can be a and b Hypotenuse: the longest side, opposite the right angle Only works for Right Triangles http://www.youtube.com/watch?v=uaj0XcLtN5c

Equations for Finding Side Lengths

Identify the legs and hypotenuse

Find the Length of the Unknown Side Is the unknown side a leg or the hypotenuse? Which equation should be used?

Identify the unknown side as a leg or hypotenuse. 2 Identify the unknown side as a leg or hypotenuse. 2. Find the length of the unknown side. Write your answer as a simplified radical

Similarity Proof of the Theorem http://www.youtube.com/watch?v=pVo6szYE13Y

Find the area of an isosceles triangle Step 1:Draw a sketch of the isosceles triangle. The altitude of a triangle is the height of the triangle Step 2:Use the Pythagorean theorem to find the height Step 3: Find the Area

Find the area of an isosceles triangle Sketch the Isosceles Triangle Find the Height Use Pythagorean Theorem Find the Area

Your Turn Find the area of the triangle.

Pythagorean Triples Pythagorean Triple: A set of three positive integers a, b, and c that satisfy the equation

Find the Unknown side of the right triangle Hint: Check for Pythagorean triples

Pythagorean Rap http://www.teachertube.com/viewVideo.php?video_id=87461

Assignment Pg 436 # 1-25 odd, 31, 32