This zipped folder contains
• A powerpoint file that will illustrate how similar triangles are formed when the altitude is drawn from the vertex of the right angle to the hypotenuse.
• A PDF file with a full set of directions on how to use the smart notebook file.
In the Smart Notebook file
• Slide 2 is a Do Now where students write ratios and proportions for three sets of two similar polygons.
• Slides 3 and 4 have an optional hands-on approach to generating the triangles to define the geometric mean.
• Slide 5 shows a rectangle divided into three similar triangles. This figure comes from the hands-on activity in slides 3 and 4. Students are asked to rearrange the three triangles to illustrate that the figures have the same size and shape.
• Slide 6 shows the rectangle and two of the three triangles. Students must locate the measures from the rectangular figure to the two triangles and then set up proportions to solve for x.
• Slide 7 shows the rectangle and two of the three triangles with only numbers this time. It is actually the solution to slide 6. Students are asked to see if the numbers make sense. Students should think about similar triangles and proportional sides.
• Slide 8 introduces the term GEOMETRIC MEAN using the same picture from slide 6 and 7.
• Slide 9 through 13 are addition geometric mean questions to be solved by the students.
• Using slide 14 you can bring the whole lesson together by moving the various measurements.
• Students will be guided in setting up the ratio that leads to the geometric mean.
The identical file is also available in my store as a Smart Notebook file: “Geometric Mean - Building Understanding - SN”.