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 375 ft, CB equals 325 ft, and GB equals 425 ft, point E is outside parallelogram and segments BE and PE form triangle BPE where BP equals 225 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)

By AA similarity criterion)

Step-by-step explanation:

Given: GRPC is a parallelogram.

GC = 375 feet, BC = 325 feet, BP = 225 feet, BG = 425 feet

To find: a pair of similar triangles. criterion of similarity and BE, PE

Solution:

Opposite sides of a parallelogram are parallel.

As ,

(if lines are parallel then alternate interior angles are equal)

As ,

(if lines are parallel then alternate interior angles are equal)

So, (by AA similarity criterion)

(if two triangles are similar then their sides are proportional)

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step-by-step explanation:

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.