The document discusses identifying the sides of right triangles for use with the Pythagorean theorem. It explains that the theorem only applies to right triangles, which have one 90 degree angle. The sides of a right triangle are labeled A, B, and C. Side C is always the longest side and is opposite the 90 degree angle. Side C is called the hypotenuse. The document provides examples of labeling right triangles regardless of their orientation and emphasizes correctly identifying the hypotenuse.

1. PYTHAGOREAN THEOREM
LESSON 2
Identifying the Sides of a Right Triangle

2. 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

3. Different 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.

4. 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.

5. Right Triangle
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.

6. 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.

7. Example of three labeled sides.
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.

8. 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.

9. Examples of a right triangle with hypotenuse.
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.

10. 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.

11. 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.

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

13. More Practice
More triangles to practice labeling.

14. 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.

15. 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.