SIMILAR TRIANGLES

1)    Are any two equilateral triangles similar? Why or why not?
 
 
 

2)    Are any two isosceles triangles similar? Why or why not?
 
 
 

3)    A flashlight beam is directed horizontally at a flat vertical screen.  A triangle with side lengths 4, 5, and 6 is positioned between the light and teh screen,
        parallel to the screen.  List two sets of possible dimensions for the shadow.  Which theorem justifies your answers?
 
 
 
 
 
 
 

4)    Given a quadrilateral and its diagonals, prove that the ratio of the segments on one diagonal is equal to the ratio of the segments on the other diagonal if
        and only if the quadrilateral is a parallelogram or a trapezoid.
 
 
 
 
 
 

The coordinates of A, B, and C are A(0,0), B(2,6), and C(8,-2).  Are the following triangles similar to triangle ABC?  If so, state the theorem or postulate
which justifies similarity.  If not, explain why not.

5)    Triangle DEF with D(-2,12), E(-6,-4), and F(-18,0)
 
 
 
 

6)    Triangle AB'C' where the coordinates of B' and C' are double the coordinates for B and C