Pythagorean Theorem By Unknown

CAHSEE: Measurement and Geometry Strand MG 3.3 Know and understand the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, verify the Theorem by direct measurement. [ 3 questions ]

Prior Knowledge To solve an equation with a variable squared (x2)… take the square root of both sides. 2 2 -2 -2 x = 3 To simplify square roots, factor…then simplify if you have any twins. See module on Square Roots for a more elaborate review.

Right Triangle Any triangle that has an angle of 90 degrees The hypotenuse is the side opposite of the right angle. It is always the longest side of the triangle. The legs are the two sides that touch the 90o angle hypotenuse leg 90o leg

a2 + b2 = c2 The Pythagorean Theorem is an equation that can be used to find an unknown side length of any right triangle if the other two lengths are known. a and b are the measurements of the two legs. These two variables can be switched c b c is the measurement of the hypotenuse. This variable may not be switched with one of the leg measures. 90o a

Examples a2 + b2 = c2 22 + b2 = 82 (2•2) + b2 = (8•8) 4 + b2 = 64 ? 3 a2 + b2 = c2 22 + b2 = 82 (2•2) + b2 = (8•8) 4 + b2 = 64 -4 -4 4 2 a2 + b2 = c2 42 + 32 = c2 (4•4) + (3•3) = c2 16 + 9 = c2 5 = c ? 8

Sample Problem What is the value of x in the triangle below? 6 8 36 d) a2 + b2 = c2 82 + x2 = 102 (8•8) + x2 = (10•10) 64 + x2 = 100 -64 -64 10 8 x Answer: a

Sample Problem The hypotenuse of a right triangle is 13 cm. If one leg is 12 cm, what is the measurement of the other leg? a) b) 5 c) 25 d) a2 + b2 = c2 122 + b2 = 132 (12•12) + b2 = (13•13) 144 + b2 = 169 -144 -144 Answer: b

Worksheet Time! We will be walking around to help you. If we aren’t getting to you, please raise your hand. We will start the quiz at 10:40!

Quiz 1. What is the Pythagorean Theorem 2. Which side of the hypotenuse of the triangle? 3. What is the measure of side x? 5 3 x