Session 5, Part A:
Indirect Measurement With a Transit

In This Part: Similar Triangles | Using Similar Triangles | Measuring Distances

If we have actual measures for at least one of the similar triangles, and we also know the scale factor or ratio that links the two triangles, we can use proportional reasoning to determine the measure of the unknown side(s) on the other triangle. This unknown side corresponds to the object or feature of the object we're trying to measure.

In the following example, triangle ABC is similar to triangle DEF. In the following example, triangle ABC is similar to triangle DEF. To find the length of x, you set up a proportion as shown below. (Notice that x is perpendicular to side a, which will help us with calculations.)

When we use similar triangles to measure indirectly, we usually collect some measurements from a triangle that can be imagined using landmarks (the lengths of some of the sides and/or the measure of some of the angles) and then draw a similar triangle on paper. We need adequate information to make sure that we are dealing with a unique triangle; knowing the length of one side of a triangle would not be enough information to draw a similar triangle, but knowing two angles and one side would be. We also need to know the ratio that links the corresponding sides in the two similar triangles as you've seen above. We will explore this process in greater detail in the next section.

 Session 5: Index | Notes | Solutions | Video