part a: triangles gcb and epb
part b. sides cg and rp are parallel by definition of parallelogram.
angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.
part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.
calculation of be:
gb/be = cb/bp
(400 ft)/be = 300/200
(400 ft)/be = 3/2
3be = 2 * 400 ft
3be = 800 ft
be = 800/3 ft
calculation of pe:
gc/pe = cb/bp
(350 ft)/pe = 300/200
(350 ft)/pe = 3/2
3pe = 2 * 350 ft
3pe = 700 ft
pe = 700/3 ft