(03.06 MC) The diagram below models the layout at a camival where G, R, P, C, B, and E are various locations on the grounds. GRPC is a parallelogram
G
R
400 ft
450 ft
350 ft
B
250 ft
С
Р
E
Part A: Identify a pair of similar triangles. (2 points)

(This has all Part A, B, and C)

Part A: Triangles CGB and PEB are both similar triangles.

Part B:

I know triangles CGB and PEB are both similar triangles because GE bisects line PC by definition of a segment bisector—making B the midpoint by the definition of a midpoint.

They both share Angle B by the reflexive property.

Angle GBC is congruent to Angle PBE by the Vertical Angles Theorem.

Angle CGB is congruent to Angle PEB by the Alternate Interior Angles Theorem.

Triangle CGB is similar to Triangle PEB by the AA Similarity Postulate. 

Part C:

 PB= 250 because it is given.

Since we already proved that CGB and PEB are both similar triangles then their corresponding sides should be proportional. Scale factor is 1.4 because since we already have PB which is 250 we can divide it by CB to get our scale factor of 1.4. Now to find the distance from BE and PE. To find BE we know the similar corresponding side is GB, so we would plug in (250/350)x 450=321.4. For PE, we know the corresponding side is CG, so we would plug in(250/350)x400=285.7.

To justify your answer simply divide 400/285.7 and 450/321.4 we would get the scale factor of 1.4. Just as 350/250=1.4. 

Side PE — 285.7

Side BE—321.4

Step-by-step explanation:

Took the test and got it right. Hope this helped!

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step-by-step explanation:

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