how can i prove that two figures are similar?

Question

Hi,

I have two figures in a graph and i have to prove that the figures are similar.They both look the same but one of them is smaller.I know that in order to prove that this two figueres are similar the angles must be congruent so i am using the slope formula to prove that they are similar.

My question is Does every slope of corresponding sides have to be equal in order for two figures to be similar?

 

 

Answer 1

Daisy, you can use SSS similarity.  If you can prove the ratios of all three of the corresponding sides are equal Then the triangles must be similar.  You can use the distance formula to compute the lengths.

Answer 2

Hi Daisy;

One figure could be a rotation, reflection or translation of the other.

 

If one figure is a rotation of the other, then the three slopes would likely be different.

 

If one figure is a reflection of the other, the slopes would be negatively identical.

 

If one figure is a translation of the other, the three slopes would be identical.

 

Please comment on whether the two figures are rotations, reflections or translations of the other.