Triangles tend to be the most popular geometric figure on the ACT and SAT simply because they have so many “secret” properties. Get ready for the test with our guide to five of the more commonly tested concepts.
The height of the triangle can be found outside the triangle.
This important fact is often forgotten by test takers, and may be integral to finding the area of an obtuse triangle.
Similar triangles are often hidden.
Because similar triangles have identical angle measurements and proportional side lengths, recognizing them can help you use the measurements of one to find the measurements of the other.
Pythagorean triples (3:4:5, 5:12:13, and 8:15:17) are frequently used with right triangles.
These time-saving sets of numbers and their multiples fit perfectly into the Pythagorean Theorem; by recognizing a 3:4:5 triangle, you can identify the length of a missing side of the right triangle without doing any calculations.
The height of an equilateral triangle is one-half the side length times the square root of three (½ s√3).
This is because there are two 30:60:90 triangles hidden in an equilateral triangle.
The diagonal of a square is the length of the side times the square root of two (s√2).
This is because there are two 45:45:90 triangles hidden in an equilateral triangle.