Similar Triangle Lab
This is a chance to construct your own pairs of similar triangles using AA, SSS~, and SAS~. I hope you gain a deeper sense of similarity from this, a deeper appreciation of why triangles with those characteristics really are similar, and more skill at constructions.
Before constructing similar triangles, first get some experience building the raw materials you'll need: congruent angles and proportional sides. Then you'll construct the three pairs of similar trianges. After each construction, drag points around to convince yourself that the triangles stay similar, and also because it's so much fun.
Each activity has its own button below. If you get stuck, please visit the hints page.
- Raw materials: construct congruent angles. When you use the "angle with given size" widget, you will want to specify the angle and clockwise/counterclockwise. For the angle, in this lab we will always use the Greek letter name for the angle. To get those Greek letters, use the pulldown with the α on it. When you build the angle, you get a new point with a prime (') after its name. You have to draw the ray from the vertex through that point yourself using the "ray through two points" widget. Once you are done, drag points around to make sure the angles are still congruent.
- Raw materials: construct pairs of sides in proportion.
The easiest way I know to do this is to start by using the input window (near the bottom) to
create a name for the ratio you want. Type
ratio=distance[D,E]/distance[A,B]. Then you can just typeratiowhen you want that ratio. After that, you need to create a circle of the desired radius centered around the point you want the segment to start from. In this exercise select the "circle with center and radius" widget. Click on point E, the center. For the radius, typedistance[B,C]*ratio. Finally use the "segment between two points" widget to construct a segment from E to a random point on the circle. Do not use the 'segment with given length from point' widget; it will not work in the other constructions. Once you are done, drag points around to make sure the sides are still in proportion. - Use the AA (angle angle) theorem to build △DEF ~ △ABC. (hints)
- Use the SSS~ (side-side-side) theorem to build △DEF ~ △ABC. (hints)
- Use the SAS~ (side-angle-side) theorem to build △DEF ~ △ABC. (hints)