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Discover the Pythagorean Theorem

Subjects

• Geometry

Grades

• 6-8

Brief Description

• understand the Pythagoras theorem and learn about its use.

Keywords

Materials Needed

• cardboard
• scale
• protactor
• pen or pencil
• scissors or cutter blade
• paper
• calculator
• ladder
• measuring tape

Lesson Plan

Organize students into groups of four or five. Discuss the terms right angle, triangle, sides, and hypotenuse with students.

Ask students in each group to use cardboard to make cutouts of right-angle triangles.

Tell students to measure the sides and hypotenuse of each triangle to the nearest millimeter and convert the measurements to centimeters. Challenge students to observe their triangles and work in their groups to discover a relationship between the two sides and the hypotenuse of the triangles. Let them think of all the possible ways of relating the three sides. Allow them to make extensive use of calculators.

As soon as students find the relationship between the two sides and the hypotenuse, have them tabulate the following information for each triangle in their group:

• Measurements of sides a, b, and hypotenuse c
• Computations: squares of a, b, and c
• Relationship observed

Students should observe that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Tell them that this is known as Pythagorean Theorem or the Theorem of Pythagoras. Also, discuss the converse of the theorem. Tell students that these three positive integers a, b, and c are called a Pythagorean triplet.

Extension Activity
This activity will provide a practical application of the Pythagorean Theorem.

• Bring a ladder to the classroom and ask students to measure its length. Place the ladder against a wall and measure the distance between the foot of the ladder and the wall. Challenge students to determine how high on the wall the ladder reaches.

Assessment