Correspondence ABC ↔ DEF of ABC and ΔDEF is similarity. If AB + BC = 10 and DE + EF = 12 and AC = 6, then DF………..

Given: AB + BC = 10,

DE + EF = 12 &

AC = 6

The correspondence ABC ↔ DEF is similarity between ∆ABC and ∆DEF.

To find: DF = ?

From ∆ABC and ∆DEF, the correspondence ABC ↔ DEF is a similarity.

Now by definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.

⇒

⇒

⇒

By reciprocating on both sides,

⇒

⇒

⇒

⇒ DF = 7.2

Thus, option (c) is correct.