Flag Pole Estimation Project
H. Leblanc, R. Sampson, C. Fischer, R. Malmberg
The angle from the mirror to the person's eyesight and the angle from the mirror to the top of the flag pole are reflected angles which makes them congruent angles. The angles from the person to the mirror and from the mirror to the flag pole are perpendicular to the ground creating a 90 degree angle on both sides making them congruent. These are the two angles that signal a similar triangle. This uses the property AA similarity.
The Pencil-Person technique is an estimation technique to figure out how tall an object is in the distance. The height of the person standing next to the pole is estimated according to what they think they are (like if the person thinks they're around 5 foot, it's an easy estimation to say they're 5 foot and compare them to the pole). The person who's height is being used stands next to the pole and another person goes a decent distance away with a pencil to measure the person against the pole. When the person who's height is being used is around the size of the pencil (at the distance), then the height of the pole is measured by how many "pencils" it takes to reach the top.