Question

Describe whether the triangles are similar for 30 points

Answer 1

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

$\text{Not similar or not necessarily similar}\\\\180^o-(90^o+30^o)=180^o-120^o=60^o\neq50^o\\\\\text{different angles}\\-------------------------------$

$Similar:\\\\\triangle ABC\sim\triangle FED\qquad\boxed{SSS}\to side-side-side\\\\\dfrac{15}{5}=\dfrac{12}{4}=\dfrac{9}{3}\\\\3=3=3\\-------------------------------$