Moving with Algebra Sampler

25 Pythagorean Theorem Geometry Finding the Pythagorean relationship in right triangles Lesson Plans 218 ©MathTeachersPress, Inc. Reproduction by anymeans is strictly prohibited. 34 The PythagoreanTheorem Pythagoras, a Greek mathematician, discovered a special property about right triangles.This property relates to the square which can be drawn on each side. The right triangle below has sides of 3, 4 and 5. 3 5 4 The shorter sides, 3 and 4, are called the legs of the right triangle.The longest side, 5, is called the hypotenuse. The hypotenuse is the side opposite the right angle. 3 2 = _____ 4 2 = _____ 5 2 = _____ 3 2 + 4 2 = _____ 5 2 = _____ Describe this relationship (known as the PythagoreanTheorem): ___________________________________________________________________ ___________________________________________________________________ Three sides of a triangle are given.Is the triangle a right triangle? 1. 5, 12, 13 4. 5, 7, 9 2. 4, 5, 6 5. 9, 12, 15 3. 6, 8, 10 6. 7, 24, 25 Find the legs and hypotenuseof the right triangle formed by these squares. 7. legs = _____ hypotenuse = _____ 8. legs = _____ hypotenuse = _____ 9 16 25 25 25 In a right triangle, the sum of squares on the legs equals the square on the hypotenuse. yes no no yes yes yes 6, 8 10 9, 12 15 Objective: To find the Pythagorean relationship in right triangles. Materials: Centimeter Graph Paper (Master 4), scissors, glue Vocabulary: square of a number, exponent, factor, Pythagorean theorem, legs, hypotenuse Discover the Right Triangle Pattern In this activity, students find the squares of numbers from 1 to 10. Each student or small group will need a sheet of centimeter graph paper and scissors. Have students outline and cut out 10 squares having sides of 1, 2, 3, …, 10 cm. Display a 1-centimeter square and describe the number of units on each side. This is the smallest square shape we can make with these squares. Each side of the square has a unit of 1. How many units on the horizontal side? (1) on the vertical side? (1) How many small squares in the whole figure? (1) Write on the board: The square of 1 or 1 squared or 1 2 means 1 1 = 1 Have students complete the following table: Vertical x Units Horizontal Squares Relationship 1 1 1 1 1 2 = 1 1 = 1 2 2 2 4 2 2 = 2 2 = 4 . . . . . . . . . . . . 10 10 10 100 10 2 = 10 10 = 100 Try forming a right triangle by connecting the sides of any 3 of your squares. How many different right triangles can you make? (2) Ask students to describe each right triangle they find. (Students will find the 3-4-5 right triangle and the 6-8-10.) 3 4 5 There is a special pattern for the sides of every right triangle. Study your squares to find the pattern. (The sum of the squares on the 2 small sides of a right triangle equals the square on the large side.) Read the top of the page with the class. Ask students to circle the side that would be the hypotenuse (the longest side) in each of the problems 1 to 6. Ask volunteers to use the words “if” and “then” to describe how they will know if the sides form a right triangle. (In problem 1, if the sum of the squares of 5 and 12 equals the square of 13, then the triangle is a right triangle.) Skill Builders p. 186 Sample Lesson Geometry & Measurement Unit 4