Consider the two triangles. How can the triangles be proved similar by the SSS similarity theorem?

Two triangles are said to be similar if the ratio between their corresponding sides is similar. It is represented by the symbol '∼'.

Answer: The two triangles can be proved similar by the SSS similarity theorem if their corresponding sides are proportional.

Let's prove the two triangles are similar by the SSS similarity theorem

Explanation:

The SSS similarity theorem states that if the three sides of one triangle are respectively proportional to the three sides of another, then the two triangles are similar.

Let the triangles be ∆ ABC and ∆ DEF

In the above tringles ratio to the corresponding sides are identical. 

⇒ AB / DE = 12 / 18 = 2/ 3

⇒ BC / EF = 8 / 12 = 2/ 3

⇒ AC/ DF = 10/ 15 = 2/ 3

We see that the three sides of triangle ABC are respectively proportional to the three sides of triangle DEF, then the triangles ABC and DEF are similar.

Hence, the two triangles can be proved similar by the SSS similarity theorem if their corresponding sides are proportional.