PYTHAGOREAN THEOREMLESSON 2

Identifying the Sides of a Right Triangle

Different Triangles

As you know there are different types of triangles

The Pythagorean Theorem only works on one kind

Here are some examples of other triangles

Triangle 1 is an equilateral triangle, which means all sides are the same length and all angles are the same. Triangle 2 is scalene so all sides and angle are different. Triangle 3 is a right triangle so it has one angle of 90 degree.

Different Triangles

Right Triangles

A right triangle means they have one angle of 90 degrees. Right triangles can also have two sides of the same length or all three sides can have different lengths. This is the type of triangle that is used for the Pythagorean Theorem. It is important that you are able to identify the types of triangles if you are going to be using the Pythagorean Theorem.

Here is an example of a right triangle. A right triangle is usually labeled and is by a square drawn into the corner with the 90 Degree angle.

Right Triangle

Identifying The Sides

All triangles have three sides. Most of the time they are labeled A, B, and C. Sides A and B are interchangeable with each other, but not with side C. Side C has several characteristics that make it unique.

Always the longest side. Always opposite the 90 degree angle. Has a special name: Hypotenuse.

Here is an example of two different right triangles with their sides labeled A,B,C. Notice that side C is always the longest and is opposite the 90 degree angle identified by the square in the corner.

Example of three labeled sides.

Hypotenuse

The longest side of a triangle is called they hypotenuse.

The hypotenuse is across from the 90 degree angle in a right triangle.

The hypotenuse is always side C of a correctly labeled right triangle.

The hypotenuse is always across from the 90 degree angle, is always the longest side and is always side c when using the Pythagorean Theorem.

Examples of a right triangle with hypotenuse.

Rotated Triangles

Don’t let the rotation of the triangle throw you off.

Remember the characteristics and rules of the hypotenuse or side C.

Side C is always the same no matter how the triangle is rotated.

Labeling Sides

Now it is time to practice labeling the sides of the triangles. The next slide has examples of several triangles that are rotated differently and have different side lengths. They are all right triangles identified by the square in the 90 degree corner. Remember the rules and characteristics of certain sides of a right triangle and label each side. If needed draw several more on the board to continue practicing.

Label each side of the triangles as sides A, B, or C.

Different Triangles

More triangles to practice labeling.

More Practice

Review

Remember the Pythagorean Theorem only uses right triangles.

The sides are labeled A,B,C. Side A and B are interchangeable. Side C is the longest. Side C is opposite the 90 degree angle. Side C is called the hypotenuse. Don’t let the rotation throw you off.

Assessment

At this time the instructor should stop the slide show and draw as many examples of right triangles as they feel appropriate to assess the learners. A rubric is provided on the website to help assess the learning of the learners.