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**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:

- 3 angles of 1 triangle are the same as 3 angles of the other (A= A’; B = B’; C = C’ )
- 3 pairs of corresponding sides are in the same ratio (a = ka’; b = kb’; c = kc’)
- 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: