Pythagorean Theorem

The Pythagorean Theorem

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. If a and b are the lengths of the legs, and c is the length of the hypotenuse, then

Exploration: Move Slider to explore the theorem.

Construction: Pythagorean Theorem

Question #1

Make a conjecture about the Pythagorean Theorem using the applet above.

Given Triangle EFG. Prove that...

Question #2

Given Triangle EFG, prove that GF²+ FG²= EG².

Converse of the Pythagorean Theorem

If the length of a triangle is a, b and c and

, then the triangle is a right-angle triangle.

Given Triangle ABC:

Question #3

Prove the converse of the Pythagorean Theorem. Hint: Apply the Angle Postulates

Closure

Pythagorean Theorem is one of the geometry topics where students are able to explore the applets by inputting different numbers, using the slider bars and calculating the Pythagorean Theorem. Also, students are able to prove the Pythagorean Theorem by applying any postulates and using the applets as their references and make any conjectures using the formula. After proving the Pythagorean Theorem, students prove the converse statement of the Pythagorean Theorem by using their prior knowledge in Geometry in High School.