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Math for Kids23 chapters | 325 lessons

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Instructor:
*Bethany Calderwood*

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

An important part of geometry is knowing how to measure shapes. The Pythagorean Theorem is used in the measurement of triangles. In this lesson, you will learn the Pythagorean Theorem and how to use it. Then you will practice on a triangle of your own.

Scientists and mathematicians like to study relationships. They study how a plant or animal relates to its environment, and how numbers relate to nature and music. When a specific relationship is found over and over, they give it a name and share the information. One example is the **Pythagorean Theorem**, which explains the relationship between the sides of a right triangle.

Before you can learn about the Pythagorean Theorem, you need to know a few terms.

A **right triangle** has one ninety-degree angle inside the triangle, which is called a right angle. Mathematicians often mark the right angle with a box. On the diagram of the triangle, the box is drawn in red.

In a right triangle, the **hypotenuse** is the side directly across from the right angle. It is the only side of the triangle that is not a part of the right angle. On the diagram, the hypotenuse is green.

An exponent appears slightly above and to the right of a number, like this: 32. A number with an exponent is actually a multiplication sentence, and the exponent indicates how many times that number appears in the multiplication sentence. So this example, 32, means 3 x 3. An exponent of 2 is read ''to the second power'' or ''squared.''

The **Pythagorean Theorem** states the relationship between the sides of a right triangle, when *c* stands for the hypotenuse and *a* and *b* are the sides forming the right angle. The formula is:

*a*2 + *b*2 = *c*2

It is read ''a-squared plus b-squared equals c-squared.''

Leila's school is having a door-decorating contest. Leila's class wants to use ribbon to divide their door into two triangles. They know the length of each side of the door. To find out how long the ribbon needs to be, they can use the Pythagorean Theorem.

Look at the picture of the door. The door is a rectangle, so the corner is a right angle. The right angle is drawn in blue. The sides forming the right angle are labeled *a* and *b*. The ribbon is drawn in blue, dividing the door into two right triangles. The ribbon is opposite the right angle, which means it is the hypotenuse. It is labeled *c*. You can see that *a* is 4 feet and *b* is 3 feet, so we can use the Pythagorean Theorem to find *c*.

*a*2 + *b*2 = *c*2

42 + 32 = *c*2

- 42 means 4 x 4, which equals 16
- 32 means 3 x 3, which equals 9
- The new equation is 16 + 9 =
*c*2

- 16 + 9 =
*c*2 - 25 =
*c*2 - Now we need to solve for
*c*. Since we learned that*c*x*c*= 25, we can use multiplication facts to realize that 5 x 5 = 25.*c*= 5. The ribbon needs to be 5 feet long.

The **Pythagorean Theorem** describes the relationships between the sides of a **right triangle**. The square of the **hypotenuse**, the side opposite the right angle, is equal to the sum of the squares of the two sides. The formula is *a*2 + *b*2 = *c*2.

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25 in chapter 2 of the course:

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Math for Kids23 chapters | 325 lessons

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- Surface Area Lesson for Kids
- Types of Angles: Lesson for Kids
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- Geometric Shapes: Lesson for Kids
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- Special Right Triangles: 3-4-5 Triangle
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