Lesson 8 7 The Pythagorean Theorem The Pythagorean

Lesson 8 -7 The Pythagorean Theorem The Py-tha’-go-rean Thee’uh-rem (named after Pythagoras)

Building squares on right angles

Pythagorean theorem • In any right triangle, the sum of the squares of the lengths a and b of the legs is equal to the square of the length c of the hypotenuse.

The Pythagorean Theorem LESSON 8 -7 Additional Examples Find the length of the hypotenuse. c 2 = a 2 + b 2 Pythagorean Theorem c 2 = 212 + 202 Substitute. c 2 = 441 + 400 Simplify. c 2 = 841 Take the square root of each side. c = 29 The length of the hypotenuse is 29 in. 8 -7

The Pythagorean Theorem LESSON 8 -7 Additional Examples Find the missing leg of the triangle. Pythagorean Theorem a 2 + b 2 = c 2 a 2 + 152 = 252 Substitute. a 2 + 225 = 625 Simplify. Subtract 225 from both sides. a 2 + 225 – 225 = 625 – 225 a 2 = 400 Simplify. a 2 = Take the square root of each side. 400 a = 20 The length of the leg is 20 ft. 8 -7

8. 7: Applying the Pythagorean theorem

Objective • We use Pythagorean theorem to solve real -world situations • Sometimes, a triangle is not obvious but you can visualize the sides of a triangle and then draw a picture Now, let’s work on a word problem.

The Pythagorean Theorem LESSON 8 -7 Additional Examples A ladder, placed 4 ft from a wall, touches the wall 11. 3 ft above the ground. What is the approximate length of the ladder? Draw a diagram to illustrate the problem. Use the Pythagorean Theorem. Use the Pythagorean c 2 = a 2 + b 2 Theorem. Substitute. c 2 = 42 + 11. 32 c 2 = 16 + 127. 69 Square 4 and 11. 3. c 2 = 143. 69 Add. c 2 = Take the square root of each side. Use a calculator. 143. 69 c = 11. 98708 The length of the ladder is about 12 ft. 8 -7

Homework Lesson 8 -7 pp. 407 -408 #s 1 -10, 15 -18, 22 -24 (Can use a calculator if c 2 is not a perfect square) Complete Activity Lab if needed.