In this series we return to classic movies to learn fundamental strategies for GMAT Success.
In the Austin Powers movies the character known as “Dr. Evil” creates an exact version of himself, only smaller, that he calls “Mini-me.” The two characters have identical proportions even though one evil villain is 8 times the size of the other. The hero, Austin Powers, quickly recognizes the similarity, despite the difference in size. This is something that you will need to be able to do on the GMAT!
If you are not familiar with “Dr. Evil” and “Mini-me, watch the following clip:
This is what similar triangles are all about! Not the evil villain stuff, but the “same proportions, different size.” When you have proven that you have similar triangles you know that any ratio of a side of one triangle to the corresponding side of the other triangle will hold true for each of the sides and even for the height of those triangles.
As you can see from the diagram below all three angles are equal. The ratio of the lengths of the triangle will remain constant. So if A:a = 2:1 then B:b and C:c and even H:h will stay at that same ratio of 2:1
Recognizing Similar Triangles
Often the biggest difficulty that people have with these similar triangle problems is simply recognizing that they are, in fact, “similar.”
Most similar triangles on the GMAT are not like the diagram above. They are actually overlapping triangles that have one angle in common. Be on the lookout for that “shared angle.” That is usually the first clue that you have similar triangles!
In addition to the shared angle look for one of these other two clues that similar triangles are present:
1) Parallel lines: If the triangle has a shared angle AND parallel lines then you have a similar triangle. For the diagram below you would be told that DE is parallel to AC. This creates similar triangles BDE and ABC.
2) Right angles: If the triangles each have a right angle AND a shared angle then you have a similar triangle. In the diagram below you see that angle “D” is shared and that angles DCE and ABC are right angles. This means that you have similar triangles ABD and CDE.
Don’t wait for the GMAT to make similar triangles as obvious as Dr. Evil and Mini-Me. Watch out for shared angles, parallel lines, and right angles. And remember that easily recognizing similar triangles is “groovy baby, yeah!”
David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.