Special Right Triangles and Common Ratios
You are likely needed to find the missing side of a right
triangle, Pythagorean Theorem is used for this purpose
c must be the longest side
a2 +b2 = c2
3
4
It turns out there are right triangle ratios that frequently
show up on the test, which, if memorized, can save you
the trouble of using the theorem and valuable time
 The 3 : 4 : 5 ratio

Rule: If the hypotenuse ________________________, then the
ratio is probably a multiple of the 3 : 4 : 5 ratio
 3:4:5
6 : 8 : 10
9 : 12 : 15

Other common ratio’s
 5 : 12 : 13
 8 : 15 : 17
 The 45 45 90 right triangle


Half of a square
Rule:
 To find the longest side, _________ the shortest side by ________
 To find the shortest side:_________ the longest side by ________
 The 30 60 90 right triangle


6
Half of an equilateral triangle
Rule:
 The longest side is ________ the shortest side
 The middle side is the shortest side ____________________
5
10
5
3/5
6
4 2
4/5
3
9x
50
15x
40
3
2
5