Question

Is △PMR similar to △SMN ? If so, which postulate or theorem proves these two triangles are similar?

​A. △PMR ​ ​is similar to ​ △SMN ​ ​ by the ​​​ ​ SSA Similarity Theorem ​.

​B. △PMR ​ ​is similar to ​ △SMN ​ ​by the ​​ ​ SAS Similarity Theorem ​.

​C. △PMR ​ ​is similar to ​ ​ ​ △SMN ​ ​by the​ ​ SSS Similarity Theorem ​​.

​D. △PMR ​ ​is not similar to △SMN ​​.

Answer 1

In triangles PMR and SMN, corresponding sides are in same proportion, that is

`(MS)/(MP) = (MN)/(MR)`

And there is a one common angle in both triangles too, which is angle M .

And that angle is the including angle .

So the two triangles are similar by SAS .