Question

The Diagram below models the layout at a carnival where G,R,P,C,B and E are various locations on the grounds. GRPC is a Parallelgoram. Part A. Identity A pair of similar Triangle Part B. Explain how you know the trigales from part A are similarPart C. Find the distance from B to E and from P to E. Show your work.

Answer 1

We want to identify what pair of triangles are similar on the figure shown.

For doing so, we will use what we are given: GRPC is a parallelogram, and the measures on the graph, to find some values.

We have that:

$GR=CP=CB+BP=325ft+225ft=550ft$

Also,

$GC=RP=375ft$

Part A and B

For this part, we will identify similar triangles. We say that:

$\begin{gathered} \Delta GCB\sim\Delta BEP \\ \Delta GCB\sim\Delta GRE \end{gathered}$

First, we will show that the triangles GCB and BEP are similar. This happens because the angles

$\angle EBP\cong\angle CBG\text{ as they are opposite by the vertex}$

And:

$\angle BGC\cong\angle BEP$

as the lines GC and RP are parallel (because GRPC is a parallelogram) and the line BG is a transversal to parallel lines. Thus, by the criteria AA, the triangles are similar.

Now, we will show that the triangles GCB and GRE are similar.