Question

Which theorem or postulate proves that △ABC and △DEF are similar?

Select from the drop-down menu to correctly complete the statement.

The two triangles are similar by the

Answer 1

SSS Similarity Theorem

Explanation:

The answer is SSS Similarity Theorem because there is no angles labeled.

Hope this helps! ;)

Answer 2

From the given figure:

In triangle ABC

Side AB = 3 units, Side BC = 7 units and Side AC = 6 units.

In triangle DEF

Side DE = 18 units, Side EF = 42 units and Side DF = 36 units.

In triangle ABC and triangle DEF

`(AB)/(DE) = (3)/(18) = (1)/(6)`

`(BC)/(EF) = (7)/(42) = (1)/(6)`

`(AC)/(DF) = (6)/(36) = (1)/(6)`

⇒
`(AB)/(DE) =(BC)/(EF) =(AC)/(DF)`

SSS(Side-Side-Side) similarity theorem states that if three sides in one triangle are in same proportion to the corresponding sides of the other triangle, then these two triangles are similar

then, by SSS similarity theorem;

ΔABC
`\sim` ΔDEF

Therefore, the given two triangles are similar by SSS similarity theorem