# Special Triangles

### Equilateral:

#### If QR and QS don’t change lengths and angle x is reduced in size, what would happen to side RS? angle y? angle z? Answer #5

A very important point about equilateral triangles that you should never forget it that when you draw an altitude, you have not simply created two congruent triangles.  They are 30:60:90 triangles.  Look at them on the “cheat sheet.”  The sides are always in the same ration that you see there.  This is one way the test writers tell you that a triangle is a 30:60:90; they split an equilateral triangle in half.

## Sample Questions 8.  What is the perimeter of the triangle above?

(A) 3
(B) 6
(C) 9
(D) 25
(E) 27 9.  If AB equals BC, what is the area of ABC?

(A) 12
(B) 16
(C) 32
(D) 48
(E) 64

6.  If the legs of a right triangle are of lengths 2f and 3g respectively, how long is the hypotenuse?

(A) (B) (C) (D) (E)  #7. ABC has a perimeter of 36. What is the area of the triangle?

(A) 24
(B) 32
(C) 48
(D) 64
(E) 96 10.  The sizes of the angles in the triangle above have a ratio of 1:2:3. The shortest side has a length of 2. What is the perimeter of the triangle?

(A) 16
(B) 12
(C) (D) (E) 6