Question

Describe whether the triangles are similar for 30 points

Answer 1

`Similar:\\\\\triangle STU\sim\triangle QPR\qquad \boxed{SAS}\to side-angle-side\\\\m\angle SUT=m\angle QRP\\\\(10)/(4)=(20)/(8)\\\\L_s=(10)/(4)=(10\cdot2)/(4\cdot2)=(20)/(8)=R_s\\-------------------------------`

`\text{Not similar or not necessarily similar}\\\\180^o-(90^o+30^o)=180^o-120^o=60^o\\eq50^o\\\\\text{different angles}\\-------------------------------`

`Similar:\\\\\triangle ABC\sim\triangle FED\qquad\boxed{SSS}\to side-side-side\\\\(15)/(5)=(12)/(4)=(9)/(3)\\\\3=3=3\\-------------------------------`