Question

Given:TM || ZWTV || SWWhich is true about Triangles ZVT, TMS, and ZWS?Triangles ZVT, TMS, and ZWS are all similar.Triangle ZVT is similar to triangle TMS only.Triangle TMS is similar to Triangle ZWS only.Triangle ZVT is similar to triangle ZWS only.No triangles are similar.

Answer 1

In this case, corresponding sides of the three triangles of the figure are similar, then we can say that all of them are similar, that is we can formulate the following ratios:

For ZVT and TMS

$\frac{ZT}{TS}=\frac{ZV}{TM}=\frac{TV}{SM}$

For ZVT and ZWS

$\frac{ZT}{ZS}=\frac{ZV}{ZW}=\frac{TV}{SW}$

And for ZWS and TMS

$\frac{ZS}{TS}=\frac{ZW}{TM}=\frac{SW}{SM}$

Then, triangles ZVT, TMS and ZWS are all similar, the first option is the correct answer