Understanding Pythagorean Theorem. Do You Remember? Find the value of each square root. 1. 2. 3. 4.

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Presentation transcript:

Understanding Pythagorean Theorem

Do You Remember? Find the value of each square root

Today’s Lesson Students will learn about Pythagorean Theorem - what it is and what it is used for.

Vocabulary Pythagorean Theorem Legs Hypotenuse Right Angle Right Triangle Square Square Root Area of a Square (A = s 2 )

Pythagoras There once was a man named Pythagoras. He lived in Greece during the 6 th century B.C. He was a philosopher & mathematician. He and his students believed everything was related to math. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

Right Triangles Recall that a right triangle is a triangle with a right, or 90º, angle. The longest side of a right triangle is the side opposite the right angle. We call this side the hypotenuse. The other two sides are called the legs. The right angle of a right triangle is often marked with a square.

What is Pythagorean Theorem? A Theorem is a law or rule. The Pythagorean Theorem is basically the relationship between the three sides of a right triangle. Let ‘s see if you can figure out the rule.

What is Pythagorean Theorem? Make a Right Triangle on your grid paper with legs that are 3 units and 4 units long. 3 4 ?

What is Pythagorean Theorem? Let’s draw squares on each leg. 3 4

What is Pythagorean Theorem? Can anyone see the relationship between the sides and the hypotenuse? 3 4 A=16 A=9 A=25

What is Pythagorean Theorem? Let’s try some more For the following problems: 1.Make and cut out a triangle with the leg lengths given. 2.Make and cut out squares on the legs and the hypotenuse. 3.Find the area of the squares. 4.Glue it all on your colored paper. 5.Once you’ve done all the problems, make your own Theorem (rule).

What is Pythagorean Theorem? Leg 1Leg 2 Area of square on Leg 1 Area of Square on leg 2 Area of square on hypotenuse What is the rule?________________________________________________ ______________________________________________________________ ______________________________________________________________

What is the Pythagorean Theorem? The Pythagorean theorem is this: a b c b2b2 a2a2 c2c2

a2a2 b2b2 c2c2 + =

3 4 Area = 9 Area = 16 Area = ?Area = 25 What is the length of the hypotenuse? How do you know? 5 Using Pythagorean Theorem to Find missing Sides

Finding Missing Hypotenuse Using the Pythagorean Theorem Let’s try some more For the following problems: 1.Draw a triangle with the leg lengths given. 2.Draw squares on the legs and the hypotenuse. 3.Find the area of the squares. 4.Find the length of the hypotenuse.

Finding Missing Hypotenuse Using the Pythagorean Theorem Leg A Leg C Area of square on Leg 1 Area of Square on leg 2 Area of square on hypotenuse Length of Leg C Hypotenuse

Finding Missing Hypotenuse Using the Pythagorean Theorem 9 12 Area = 81 Area = 144 Area = 225