On the SAT, triangles are referred to on the exam by their three different points. Usually this will have the symbol of a triangle in front of the various points. All three angles of a triangle should always add up to 180°. Also, the perimeter of a triangle is found by adding the lengths of the three sides.
Sometimes triangles will have odd numbers for their side lengths, including square roots. It is simply a matter of adding these up and looking for the answer choice that best reflects the weirdness. Reading the question carefully and slowly also helps.
Right Triangle
A right triangle is one where one of the angles is equal to 90°. On a right triangle, the base and the height are the two sides that meet at the 90° angle. These two sides are the legs of the triangle while the opposite is the hypotenuse. The corner of the 90° angle will always point to the hypotenuse.
If two sides of the right triangle are known the third can be found with the Pythagorean Theorem (a2 + b2 = c2) where a is a leg, b is a leg and c is the hypotenuse. An interesting fact is that the hypotenuse will always be the longest of the three sides on a triangle.
Isosceles Triangle
An isosceles triangle is one where two of the sides are equal and it has two equal angles as a result of this.
Equilateral Triangle
An equilateral triangle is one where all of the three sides are equal in length and all three angles are also equal.
Scalene Triangle
Scalene triangles are those where none of the sides or angles equal each other. It is good to note that two sides (any two) must add up to a number greater than the other third side of the triangle.
Special Right Triangles
A triangle known as a 30-60-90 triangle will have one 30° side, one 60° side, and one 90° side. The short side will be the side opposite of the 30° angle. It is a good idea to always go through the shortest side with these triangles because it doesn't take long to find a different side.
TIP: Do not ever use special angles (like 45 ot 90 for example) when using numbers in a question. This can cause repeat answers that will require new angles to be used and can waste time.
Some common sides of right triangles on the SAT math exam are...
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
Similar/Congruent Triangles
When all three angles of two different triangles are equal, the two are considered "similar triangles," which means their sides are in proportion. If two triangles have sides that are all in proportion, their angles will also be equal to each other.
For similar triangles, the ratio of the areas is the ratio of their sides squared. Therefore, two similar triangles with sides in the proportion 3/4 will also both have areas with the proportion 9/16.
