options: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
problem_activity: Task
Pablo is practicing bank shots on a standard 4 ft.-by-8 ft. pool table that has a wall on each side, a pocket in each corner, and a pocket at the midpoint of each eight-foot side.
Pablo places the cue ball one foot away from the south wall of the table and one foot away from the west wall, as shown in the diagram below.  He wants to bank the cue ball off of the east wall and into the pocket at the midpoint of the north wall.
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At what point should the cue ball hit the east wall?
After Pablo practices banking the cue ball off of the east wall, he tries placing the eight-ball two feet from the east wall, as shown in the diagram below, so that if he shoots the cue ball exactly as he did before, the cue ball will strike the eight-ball directly and sink the eight-ball into the north pocket.  How far from the north wall should Pablo place the eight-ball?
[IMG]


correct_option_index: 1