7 1 Apply the Pythagorean Theorem Before You

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 p In a right triangle, the sum of the squares of the measures of the legs equals the square of the hypotenuse. Only works for Right Triangles http: //www. youtube. com/watch? v=uaj 0 Xc. Lt. N 5 c

Equations for Finding Side Lengths

Identify the legs and hypotenuse

Find the Length of the Unknown Side 1. 2. Is the unknown side a leg or the hypotenuse? Which equation should be used?

1. 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 p http: //www. youtube. com/watch? v=p. Vo 6 s z. YE 13 Y

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

Find the area of an isosceles triangle 1. Sketch the Isosceles Triangle 2. Find the Height 1. 3. Use Pythagorean Theorem Find the Area

Your Turn Find the area of the triangle.

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

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

Pythagorean Rap p http: //www. teachertube. com/view. Video. p hp? video_id=87461

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