 Posted By StudyGate
How to Prove There are 2 Similar Triangles

In the whole, wide world of geometry, there are so many shapes and sizes of triangles that you might think they’re all exactly the same, or that they’re all completely different. Not necessarily! Two triangles must share precisely specific traits in order to be deemed similar. If you’re faced with the puzzle of determining if there are two similar triangles, there are three different paths you can take to solve the mystery.

## Path 1: Use the Angle-Angle (AA) Method

If you can determine the angle measurement of at least two angles from each triangle, the AA method is your best chance of solving the similarity mystery. If two angles of one triangle are the exact same measurement of the same two angles of the other, they must be similar. If this doesn’t make sense, it might help to contact an online math tutor for additional explanation.

## Path 2: Use the Side-Side-Side (SSS) Method

The SSS method is most helpful when you are given, or can determine, the length of all three sides of both triangles. If all sides are specifically proportional to the corresponding sides of the other, then those two triangles must be similar. For example, if one triangle has a hypotenuse of 3 inches, and the second has a hypotenuse of 6 inches, those two sides are proportional because 6 is exactly twice the length of 3. If the other corresponding sides of the triangle are proportional, the triangles are similar and the mystery is solved.

## Path 3: Use the Side-Angle-Side (SAS) Method

When you’re faced with two triangles that have at least one given angle measurement, and two given side measurements, the SAS method is your best bet. If the corresponding angles have the exact same measurements, and the corresponding sides are proportional to one another, then those triangles must be similar. Just remember that the measured angle from one triangle must be in exactly the same place as the measured angle from the other, and the same principle applies to the measurements of the two sides as well. 