Question

given ex is parallel to line tw prove rs times st equals as times sx

Answer 1

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle XRS and triangle TWS are similar by AA similarity theorem

that means

XR/TW=RS/WS=XS/TS

so

RS/WS=XS/TS

multiply in cross

RS*TS=XS*WS

rewrite

RS*ST=WS*SX -----> is proved