Answered

Triangle abc has been dilated to form triangle a'b'

Cif sides ab and a'b' are proportional, what is the least amount of additional information needed to determine if the two triangles are similar?

Verified Answer :

Edufirst

It is needed at least one more piece of information.

If you call k the ratio a'b' / ab , the addtional information may be tha cb' has the same ratio to cb or that ca' has the same ratio  to ca.

It migh also be that the angle at the vertex C has not changed.

Answer: The answer is given below.

Step-by-step explanation: We are

given that triangle ABC has been dilated to form triangle A'B'C'.

Also, the sides AB and A'B' are proportional. We are given to find the least amount of additional information to prove that the two triangles are similar.

Since, here dilation is taking place, so for the two triangles to be similar, we need at least one pair if corresponding sides proportional.

That is, either BC proportional to B'C' or CA proportional to C'A'. We can write

\(\dfrac{AB}{A'B'}=\dfrac{BC}{B'C'}=k\)

Or

\(\dfrac{AB}{A'B'}=\dfrac{CA}{C'A'}=k.\)