## You Can't Go Wrong with a Right Triangle 1

### Linda Knowles

#### Description

Students will develop an understanding of the Pythagorean Theorem and use it to find the missing side of a right triangle.

#### Objectives

Associates verbal names, written word names, and standard numerals with integers, rational numbers, irrational numbers, real numbers and complex numbers.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

-Pencil, paper, calculator
-Ruler
-Construction paper

#### Preparations

1. Out of construction paper, cut out 4 right triangles (marking the 90 degree angle on each) and one triangle that is not a right triangle for each group.
2. Locate a ruler and calculator for each group.
3. Run off one copy of File Document #1 for each group.
4. Run off one copy of File Document #2 for each student.

#### Procedures

This lesson is part of a series entitled You Can’t Go Wrong With a Right Triangle I, II, and III.

Prior knowledge required: Students should recognize a right triangle ( a triangle with a 90 degree angle) and be able to measure its sides. They should also be able to square a number, solve an equation and use a calculator to find square roots.
1. Gain their attention by telling them that the theorem they are about to learn, the Pythagorean Theorem, has long been credited to Pythagoras (572-497 B.C.), a Greek mathematician and philosopher. Tell them that the REAL (but not really) story of this theorem stems from an old Indian legend, which goes like this: Two braves were arguing about which of them had the best wife (squaw). One squaw was sitting on the very rare hippopotamus hide her husband had given to her. The other brave had two wives who were just sitting on regular buffalo hides. Their argument went on and on until the first brave settled the argument by saying, “Why, my wife is so wonderful that the squaw on the hippopotamus hide is equal to the sum of the squaws on the other two hides!” Be sure to tell this story again after the group activity.

2. Review the parts of a right triangle: legs, hypotenuse, right angle and acute angles. Make sure that they know that the hypotenuse is always the longest side (opposite the right angle) and will be referred to with the letter c. Also tell them that the lengths of the legs will be referred to with the letters a and b.

3. Place students in groups of three.

4. Pass out to each group four large right triangles made out of construction paper, one triangle that is not a right triangle, a ruler, a calculator and a worksheet. (File Document #1)

5. Tell each group to put to the side the non-right triangle until later in the lesson.

6. One student will measure the sides of the right triangles, correct to the nearest ¼ inch or millimeter. One student will record the lengths of the sides and the third student will do the computations called for on the worksheet. Record the name of each group member on the worksheet.

7. Circulate around the room to help as needed.

8. After all calculations on the right triangles are completed, instruct them that the first group to come up with the correct conclusion (a2 + b2 = c2) will receive a reward (candy, homework pass, 2 points on a test, etc.).

9. Retell the story and tell them that a good way to remember the Pythagorean Theorem is to say to themselves “The squaw on the hippopotamus hide is equal to the sum of the squaws on the other two hides.”

10. Have each group do the same measurements and calculations on the triangle that is not a right triangle and make a conclusion about the relationship between a2, b2, and c2 on this triangle.

11. Reinforce the fact that the relationship a2 + b2 = c2 only works on a right triangle.

12. Collect the group papers.

13. Pass out the second worksheet (File Document #2) to each student.

14. Review on the board several examples of how to use the Pythagorean Theorem to find the missing side of a right triangle.

15. Circulate around the room to help as needed.

16. Assign the remainder of this worksheet as homework.

17. Collect the worksheet the next day.

#### Assessments

The teacher will observe the group activity and grade the papers turned in from each group on a percentage basis. Each student in the group will receive the same grade for this part of the activity. The second worksheet (one done by each student) will be graded on a percentage of correct answers.

#### Attached Files

2 worksheets.     File Extension: pdf