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 _________________

A. SSS Similarity Theorem
B. SAS Similarity Theorem
C. AA Similarity Postulate

Answer 1

Answer: SSS similarity (choice A)

The SSS stands for "side side side", so saying "SSS similarity" means the three corresponding sides are in the same proportion as each other.

Divide each side of DEF by its corresponding side of ABC

DE/AB = 18/3 = 6

EF/BC = 42/7 = 6

FD/CA = 36/6 = 6

We get 6 each time we divide, so the scale factor is 6. Each side of DEF is 6 times longer compared to its corresponding counterpart back in ABC.

Side note: the area of triangle DEF is 36 times larger since 6^2 = 36.