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The Pythagorean Theorem x z y
For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c
The Pythagorean Theorem Copy the triangle three more times and build a square with each triangle at a corner a b c
The Pythagorean Theorem Copy the labels to the corresponding sides a b c a a a b b b c c c
The Pythagorean Theorem a b c a a a b b b c c c The Area of the big square can be found by multiplying the lengths of the sides (a + b)(a + b)
The Pythagorean Theorem a b c a a a b b b c c c
a b c a a b b c c c
a b c
Example 1 For this example we will be given both legs and will be trying to find the hypotenuse 10 x 6
Example 1 Setup the equation using the Pythagorean Theorem: (Small leg) 2 + (Large leg) 2 = hypotenuse 2 10 x 6
Example 2 For this example we will be given a leg and the hypotenuse and will be trying to find the other leg 9 x 4
Example 2 9 x 4 Setup the equation using the Pythagorean Theorem: (Small leg) 2 + (Large leg) 2 = hypotenuse 2 4 2 + x 2 = 9 2
Pythagoras Bingo. Pick 8 from the list C no 16124yes Pythagorean triple Hypotenuse Pythagoras theorem.
The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.
Things to do: ♥Make a new note book ♥Get out your homework (triangle worksheet)
Pythagoras Proofs TEKS 8.07 (C): The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.
Created by G. Antidormi 2003 The Pythagorean Theorem.
EXAMPLE 4 SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of.
EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.
The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.
EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.
The Pythagorean Theorem. 8/18/20152 The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area.
Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’
Pythagorean Theorem 2 Algebraic Proofs. Pythagoras’ Proof.
Pythagorean Theorem By: Tytionna Williams.
4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA
10.5 – The Pythagorean Theorem. leg legleg hypotenuse hypotenuse leg legleg.
Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.
MA.912.G.5.1 : Apply the Pythagorean Theorem and its Converse. A.5 ft B.10 ft C. 15 ft D. 18 ft What is the value of x? x 25 ft 20 ft.
Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.
The Pythagorean Theorem
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