Question

Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF.

△ABC: AB = 10, BC = 16, CA = 20
△DEF: DE = 25, EF = 40, FD = 50
I really need someone to explain to me how to do this because i am so confused my teacher didn't give us notes and didn't explain this very well.

Answer 1

The scale factor can be found by finding the ratio of corresponding sides.  Based on the similarity statement, we know that the ratio between side AB and DE is the same as the ratio between side BC and EF, as well as betweeen AC and DF.  The ratio between sides AB and DE is 10/25 = 2/5.
The ratio between sides BC and EF is 16/40=8/20=2/5.
The ratio between sides AC and DF is 20/50=2/5.  Verifying that the same ratio applies to all corresponding sides proves that the triangle is indeed similar, and the scale factor is 2/5.