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
