Question

PLEASE HELP!!! 20 pts! Screenshotted the image it is attached

Answer 1

SAS Similarity Theorem: If one angle of the triangle is equal to one angle of another triangle and sides including these angles are proportional then the two triangles are similar.

Denote Home as point H, Park - P, Friend's house - F, Bus shop - B, Grocery store - G. To show that the triangles ΔHPB and ΔHFG are similar by SAS theorem, you should state that:
1. ∠PHB and ∠FHG are the same;
2. $\dfrac{HP}{HF}= \dfrac{HB}{HG}$.
For the second part you need to have the distance from the bus shop to his home.
In this case,
$\dfrac{10}{15} = \dfrac{6}{9} \left(= \dfrac{2}{3}\right)$
Answer: the correct choice is B.