Similar triangles

When are two triangles similar?

If some dynamic worksheets are not available, java can be download frompágina

On the next dynamic worksheet you can move the triangle ABC (red), k and α.

• Is there any relationship between the angles of the three triangles?
  

• What happens when you move k? And when you move α? Do the angles change? what about the sides?
  

• What do you have to do to make the triangle A’’B’’C’’ (green) bigger?
  

• Two triangles ABC y A’B’C’ are similar when they fulfill one of the three next:
  

1. 3 angles of 1 triangle are the same as 3 angles of the other (A= A’; B = B’; C = C’ )
2. 3 pairs of corresponding sides are in the same ratio (a = ka’; b = kb’; c = kc’)
3. An angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio.

    (Check this on the worksheet below.)

• Two triangles ABC and A’B’C’ are similar when two pairs of angles are the same:
  

On the next picture, A=A’ y B=B’, for instance.

     (Check this on the worksheet below.)

• Two right-angled triangles are similar When one of their not right angles are the same.
  

On the next picture,B=B', for instance.

    (Check this on the worksheet below.)

You can use similar triangle's theory to do the next exercises:

• With a coin!
  
• With a photo.