GRE Math: 45°-45°-90° and 30°-60°-90° Right Triangles

45°-45°-9o° Right Triangles (isosceles Right Triangles)

These triangles have side lengths in the ratio 1 : 1 :√2.

Note that the legs have the same length. Again, be on the lookout for multiples. An isosceles right triangle is formed when a square is divided in half by one of its diagonals. This is often helpful in solving geometric questions.

45°-45°-9o° Right Triangle

 30°-60°-90° Right Triangles

These triangles have side lengths in the ratio 1 :√3:2.

When an equilateral triangle is divided in half, the result is a 30°-60°-90° triangle.

30°-60°-90° Right Triangle

Important Notes:

Remember Pythagorean triples which are listed below :

3 – 4 – 5

6 – 8 – 10

9 – 12 – 15

5 – 12 – 13

7 – 24 – 25

8 – 15 – 17

9 – 40 – 41

Knowing these triples allows us to quickly answer the question.

45°-45°-9o° Right Triangle side lengths in the ratio 1 : 1 :√2. 

 30°-60°-90° Right Triangles side lengths in the ratio 1 :√3:2. 

Read More:

1. How to Solve "Special " Right Triangles