Hello Mr. Mike. Can you please explain how to solve Similar triangle problems? I especially find confusing identifying equal sides and making proportions. I have an example problem, please see the link below.

First, you need to know the similarity rules. Triangles are similar if you can establish that two sets of their angles are congruent (Angle-Angle), if two sets of sides are proportional and the angles between them are congruent (Side-Angle-Side), or if all three sets of sides are proportional (Side-Side-Side). In the case of the screenshot you’ve provided, we have Angle-Angle: both triangles have 90° angles and both triangles contain angle L.

Once you’ve established that you’ve got similar triangles, you kinda have to follow where the question leads—there are lots of combinations of angles and sides that could be given and/or asked for.

Continuing with the example you’ve provided, we can solve for LY using the Pythagorean theorem:


Now this is important: LY is the hypotenuse of the small triangle, but it’s the short leg of the big triangle! At this point in these questions I find it helpful to draw both triangles in the same orientation. For example, you might draw these ones like so:

Doing that makes it much easier to see that the long leg of triangle WLY will be twice the length of the short leg, just like triangle YLA.

From there, all we need to do is the Pythagorean theorem again to find LW.


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