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.

http://ibb.co/fLJ1Hc

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*.