Lori has written the conjectures below. For each one, decide if it is true or not. If you believe it is not true, find a counter example (an example that proves that the statement is false).  

1. If a triangle has a $60^\circ$ angle, it must be an equilateral triangle.

   Hint (a):

   Can a triangle have one $60^\circ$ angle and the other angles not be $60^{\circ}$?

2. To find the area of a shape, you always multiply the length of the base by the height.

   Hint (b):

   How do you find the area of a trapezoid? Think of its formula.

3. All shapes have $360^\circ$ rotation symmetry.

   Hint (c):

   What does it mean to have $360^\circ$ rotation?