Question

When we construct a triangle similar to a given triangle to a given triangle as per given scale factor, we construct on the basis of……….

a)SSS similarity
b)AAA similarity
c)Basic proportionality theorem
d)A and C are correct

Answer 1

Hint: We are told in the question that the similar triangle drawn is per scale factor so find a similarity that deals with the scale or the length of the side.

Complete step-by-step answer:
Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.
Tests to prove that a triangle is similar
Angle-Angle Similarity (AA)
If two corresponding angles of the two triangles are congruent, the triangle must be similar.

Side-Side-Side Similarity (SSS)
If the corresponding sides of the two triangles are proportional the triangles must be similar.

Side Angle Side Similarity (SAS)
If two sides of two triangles are proportional and they have one corresponding angle congruent, the two triangles are said to be similar.

Basic Proportionality theorem:
Basic Proportionality theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those two sides in the same ratio.
So, assessing all the similarities we can say that only similarity that matches with the term scale factor is SSS similarity.
Hence, option A is the correct answer.

Note: When we are checking the different ways to prove whether the triangles are similar, we might get confused with SAS similarity as it also checks using the similar sides but the difference is that it requires one angle also and we are given scale as the only factor.