PYTHAGOREAN THEOREMLESSON 2Identifying 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
Different TrianglesTriangle 1 is an equilateral triangle, which means all sides are the same length and allangles are the same. Triangle 2 is scalene so all sides and angle are different. Triangle3 is a right triangle so it has one angle of 90 degree.
Right TrianglesA 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.
Right TriangleHere is an example of a right triangle. A right triangle is usually labeled and is bya square drawn into the corner with the 90 Degree angle.
Identifying The SidesAll 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.
Example of three labeled sides.Here is an example of two different right triangles with their sides labeled A,B,C. Noticethat side C is always the longest and is opposite the 90 degree angle identified by thesquare in the corner.
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.
Examples of a right triangle with hypotenuse.The hypotenuse is always across from the 90 degree angle, is always the longestside and is always side c when using the Pythagorean Theorem.
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 SidesNow 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.
Different TrianglesLabel each side of the triangles as sides A, B, or C.
More PracticeMore triangles to practice labeling.
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.
AssessmentAt 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.