Tricky Triangles: the GMAT’s Favorite Shape!

A triangle is a three-sided shape whose three inner angles must sum to 180°. The largest angle will always be across from the longest side. Triangles are the most commonly-tested geometry topic on the GMAT!

Remember the sum of all the interior angles in a triangle will sum to 180 degrees, so you can always solve for the third angle if you know the other two.

If you’re told two triangles are similar, the corresponding angles are congruent, or equal. You can set up various proportions to the corresponding sides as well.

More essential info:essential info: the side of any triangle must be BETWEEN the sum and the difference of the other two sides.

Check out some practice problems to refresh your triangle properties on this Learnboard!

What’s the Triangle Inequality Theorem?

Triangle Inequality Theorem is fair game on the SAT, ACT, GRE, or GMAT. It’s often forgotten by test-takers, but when it pops up, you’ll be glad you know it! The theorem essentially states that the third side of a triangle must be between the difference and sum of the other two sides.

For example, if we had a triangle in which two sides were 6 and 9, then the third side must be between 3 (9-6) and 15 (9+6). The third side cannot actually equal 3 or 15, it’s important to remember.

Let’s try a practice question utilizing this math rule!

If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

A) None
B) I only
C) II only
D) II and III only
E) I,II and III

If two of the sides are 2 and 5. Then the range of possible values for the third side can be expressed as:

3 < x < 7

Perimeter is the sum of the sides. Let’s choose 3 and 7 as values for the 3rd side (even though we know they are the end-limits only) to create a range for the perimeter.

On the low end:

2 + 5 + 3 = 10

On the upper end:

2 + 5 + 7 = 14

So the perimeter range can be expressed as:

10 < x < 14

The perimeter must be BETWEEN 10 and 14. The answer is (A).

Here’s a link to a lot of great Triangle review topics if you want more Geometry practice: