Christian J.

asked • 12/14/22

Could you please help

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 400 ft, CB equals 350 ft, and GB equals 450 ft, point E is outside parallelogram and segments BE and PE form triangle BPE where BP equals 250 ft.

Part A: Identify a pair of similar triangles.

Part B: Explain how you know the triangles from Part A are similar.

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


Mark M.

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12/14/22

Araoye I.

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Without giving away the whole answer, I will mention that the lines PE and CG are parallel bases, as are GR and BP. Either gives you a pair of similar triangles. One way might be easier than the other if you are more or less comfortable with alternate/ opposite angles..
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12/15/22

1 Expert Answer

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William W. answered • 12/15/22

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Because GRPC is a parallelogram, GC is parallel to RP (also RE since RE is just an extension of RP).


Because GC is parallel to RE, then the two red angles are alternate interior angles and are congruent.


Because they are vertical angles, the two blue angles are congruent.

Because of AA~, ΔGCB ~ ΔEPB


Because they are similar, you can set up proportions:

and

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