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)

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if the ratio of their corresponding sides are equal.

From the problem, since GRPC is a parallelogram, hence:

GC is parallel to RE and GR is parallel to CP.

∠GBC = ∠EBP (vertical opposite angles are equal)

∠BGC = ∠BEP (alternate interior angles are equal)

∠BCG = ∠BPE (alternate interior angles are equal)

Since, ∠GBC = ∠EBP, ∠BGC = ∠BEP and ∠BCG = ∠BPE, we can say that triangle BCG is similar to triangle BEP by the angle - angle - angle similarity postulate.

c) Since the triangle BCG is similar to triangle BEP, hence: