This lesson (which includes a 36 slide PowerPoint presentation and 9 pages of notes to accompany the presentation) walks a student through the discovery of geometric means when an altitude is drawn to the hypotenuse of a right triangle.
The lesson begins by reviewing ratio, proportion, and similar triangles. It then introduces the student to the concept of geometric means. From there an altitude is drawn to the hypotenuse of a right triangle and the student is shown why the three triangles are similar. This is done by PowerPoint animations with the triangles being separated, rotated, and then flipped so that the corresponding sides of the similar triangles can be used to create proportions.
As a result of the triangles being similar, the student is shown how the altitude and each leg of the original triangle is a geometric mean.
Once the geometric means are established, the student is then shown how the proportions from the similar triangles leads to an algebraic proof of the Pythagorean Theorem.
This lesson is perfect to use in the classroom or placed on your classroom website so that students can access it as many times as necessary to fully grasp the concept of geometric means.
The PowerPoint is fully editable to fit your personal use and the notes are provided in Word and as a PDF. The word document is also editable to fit your personal needs.
The lesson was created using PowerPoint 2003 and MathType 6.9.