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3 years ago

I need help its urgent ASAP will mark you the brainliest

Mathematics

1 answer:

kherson [118]3 years ago

5 0

9514 1404 393

Answer:

BE = 266 2/3

PE = 233 1/3

Step-by-step explanation:

Part A: The figure has 3 triangles, all similar. In order of shortest-to-longest side lengths, they are ...

ΔBPE ~ ΔBCG ~ ΔGRE

Part B: They can be declared similar by the AA postulate. For BPE and BCG, the angles at B are vertical angles, so are congruent. The angles at C and G are alternate interior angles, so are congruent.

For triangles BPE and GRE, angle E is congruent to itself, The angles at R and P are corresponding angles, so are congruent.

(Remember, GRPC is a parallelogram, so any line in the figure is a transversal crossing parallel lines.)

Part C:

From parts A and B, we know ΔBPE ~ ΔBCG. Corresponding sides are proportional:

BP/BC = BE/BG = PE/CG

200/300 = BE/400 = PE/350

BE = (400)(2/3) = 266 2/3

PE = (350)(2/3) = 233 1/3

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