Stephen is making a map of his neighborhood. he knows the following information

The question is missing the image given to go along with it, corresponding to the map being created. The image is attached to this answer.

The side angle side (SAS) similarity theorem states that two triangles with congruent angles and sides with identical ratios then the two triangles are similar. We have various points on the map, Home (H), Park (P), Friends house (F) and Grocery store (G).

In this example, we know the angle at the point Home on the map, is shared between the two triangles. If these two triangles are similar, then the ratio of the distances HF/HG = HP/HB. We know all of these values except for the HB which is the distance from home to the bus stop. But if these triangles are similar, we can solve for that distance.

15/9 = 10/HB
HB = 90/15
HB = 6 blocks.

To determine if the triangles are similar we need to know the distance from home to the bus stop, and if these are indeed similar, that distance must be 6 blocks.

Distributive property