Question

Determine whether or not the given pair of triangles is similar and state how you know.

Answer 1

Answer:

            by SAS.  

             Yes  

Step-by-step explanation:

∠HIG and ∠JIK are vertical angles, so:

m∠HIG = m∠JIK

$\dfrac{GI}{IJ}=\dfrac{7.5}3=2.5\\\\\dfrac{HI}{IK}=\dfrac{2.5}1=2.5$

$\left\{\dfrac{GI}{IJ}=\dfrac{HI}{IK}\quad\ \wedge\quad m\angle HIG=m\angle JIK\right\}\implies \triangle HIG\sim\triangle JIK\ \ by\ SAS$