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 parallelogram.

Parallelogram GRPC with point B between C and P forming triangle GCB where GC equals 350 ft, CB equals 300 ft, and GB equals 400 ft, point E is outside parallelogram and segments BE and PE form triangle BPE where BP equals 200 ft.

Part A: Identify a pair of similar triangles. (2 points)

Part B: Explain how you know the triangles from Part A are similar. (4 points)

Part C: Find the distance from B to E and from P to E. Show your work. (4 points)

Answer 1

#A

∆BCG and ∆BPE

#B

• <B is common angle

Then

GPRC is parallelogram

• <C+<CRP=180
• <CRP+<BPE=180

From these

• <C=<BPE

Hence from AA congruence the triangles are similar

#C

• BE/BG=BC/BP
• x/400=300/200
• 200x=120000
• x=600ft

BE=600ft

And

• CG/BG=PE/BE
• 350/300=PE/600
• 350=PE/2
• PE=700ft