Answer:
A.Angles B and B' are congruent and angles C and C' are congruent .
Step-by-step explanation:
We are given that a triangle ABC has been dilated to form triangle A'B'C'.
If sides AB and A'B' are proportional .
We have to find the least amount of additional information needed to determine if the two triangles are similar.
A. If Angles B and B' are congruent and angles C and C' are congruent then the two triangles are congruent by AA- similarity theorem.
Because if two pairs of corresponding angles of two triangles are congruent then two triangles are similar.Hence. it is sufficient condition for proving two triangles are similar.Therefore, option A is true.
B. Segments AC and A'C' are congruent , and segments BC and B'C' are congruent. It is not sufficient condition for proving two triangles ABC and A'B'C' are similar because we know that if two triangles are similar then the all sides of triangle with corresponding sides of another triangle are in equal proportion.
In question we are given that side AB and A'B' are proportional but not congruent.
Hence, it is false.
C.Angle C=C' and B=B' and segments BC and B'C' are congruent.
It is sufficient but not least amount of additional information needed to determine the two triangles are similar.Therefore, it is false.
D.Segments BC=B'C' , segment AC=A'C', and angles B and B' are congruent.
It is not sufficient for proving the two triangles are similar.Because we have two angles pair with their corresponding angles are equal.But we have no information about angles which is made by two given pairs of corresponding sides .Therefore, it is false.
