Pythagorean Theorem This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in.

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Presentation transcript:

Pythagorean Theorem This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

Squares Before solving Pythagorean Theorem problems, we must understand the concept of squares and square roots. is 5 x 5 =25. 5 x 5 is written 5² base exponent 5²

Table of Perfect Squares 1² = 1 6² = 36 11² = 121 2² = 4 7² = 49 12² = 144 3² = 9 8² = 64 13² = 169 4² = 16 9² = 81 14² = 196 5² = 25 10² = ² = 225

Example: √25 = 5 ; in other words 5 x 5 = 25 √36 = 6 ; in other words 6 x 6 = 36 The square root of a number is found by asking, “What number times itself equals this?” For example: What number times itself equals 4?

Guided Practice Directions: What is the value of each squared number or letter below? 1.3² = ____ 2. 8² = ____3. 12² = ____ 4.10² = ____5. a² if a = 4 _____ 6. x² if x = 13 _____7. b² if b = 18 _____

Pythagorean Theorem Is used to find the third side of a right triangle when the other two sides are known. Key Terms: a & b are known as the legs. c is known as the hypotenuse. The hypotenuse will always be the opposite side of the right angle. The formula for solving Pythagorean problems is: a² + b² = c² a b c

Pythagorean Theorem All word problems that create a right triangle are considered a Pythagorean problem. Here are some examples of real life situation where you can use the Pythagorean theorem. Building a ramp Crossing a field Pouring a sidewalk Installing a temporary pole, etc. Leaning a ladder up against a wall/tree.

Pythagorean Theorem When you are solving Pythagorean word problems you will need to identify what sides you are looking for. The following words be used to refer to the hypotenuse, side c: diagonal direct distance directly any intermediary directions (NW,NE,SW,SE)

Lets Practice Identify which sides are legs and which side is the hypotenuse. E A C B K L J G I H F D

Let’s Practice a²+b²=c² 5²+4²=c² 25+16=c² 41 = c²  41=  c² c = a²+b²=c² 6²+b²=21² 36+b²= b²=-36 b² = 405  b²=  405 b = 20

Word Problems 18.3 feet = b 20 ft 8 ft

2. George rides a bike 9 km south and then 12 km east. How far is he from his starting point? 15 km 9 km 12 km

3. Find the length of a rectangle that has a diagonal of 25 feet and a width of 15 feet. 25 ft 15 ft c² - a² = b² 25² - 15² = b² 625 – 225 = b² 400 = b² 20 = b