Flagpole Estimation Project
Kathryn Ensminger, Jaslyn Evans, and Ryan Collins
Using AA Similarity
AA Similarity is a form of indirect measurement. In order to use the AA Similarity Theorem, the similar triangles both must have right angles between the two legs of the triangles, as well as corresponding angles between one leg and the hypotenuse of the triangle.
Example: In the flagpole assignment, AA Similarity applies because there are corresponding right angles at the bottom of the flag and the person, and there are corresponding angles where the angles meet at the mirror. The mirror provides this angle because of reflection.
The pencil/person technique provides a way to determine the estimate of the height of something without using exact measurements. In order to apply Pencil/Person to the flagpole assignment, you can take a pencil, or any other straight figure that can be used in place or a ruler, and measure a person's height by standing at a distance and finding their height on the pencil. From there, you can see how many times the person's height can be measured on a larger object, then multiply the height of the person by the number of times the height was used on the larger object.
Example: The groups in Coach Borel's geometry classes provided pencil/person measurements by determining one group member's height with a pencil and multiplying it by the number of times that height could be used to reach the top of the flagpole.