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Figure This!


Complete Solution:

The lines in the drawing show one path of a hole-in-one. The marked angles (1 and 2) have equal size. You should aim for point P.

One way to locate the proper place to aim is to think of the sidewall as a mirror. If you looked into this mirror from the tee, the hole's reflection would appear to be in the location shown in the diagram below:

As mentioned in the hint, the angle at which the ball leaves the wall will be the same as the angle at which it hit the wall. If you aim the ball at the point where the line from the tee to the hole’s image intersects the wall, then it will bounce into the hole.

This can be proven mathematically as follows: Because the two triangles on either side of the wall in the diagram are mirror images, they are exactly the same size and shape (congruent). This means that angle 2 is the same size as angle 3. Angle 1 and angle 3 are also the same size, because they are vertical angles. (Vertical angles are angles formed by two intersecting lines.) Angle 1 is the same size as angle 2 because both are the same size as angle 3. This means that the path to the hole shown on the diagram is the same path the ball will take as it bounces off the wall.

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