1. Reflections and Geometry Proofs
Making the Hole-in-One a Reality

2. 1. Outline a pentomino diagram of your choice.

3. 2. Determine where you want to place the tee (label with a dot and T)
2. Determine where you want to place the tee (label with a dot and T). Determine where you want to place the hole (label with a dot and H). H T

4. 3. Select the wall of the pentomino you will bank the ball off of and label it W1.

5. 4. With a compass, construct a dotted line from H that is perpendicular to W1. Reflect this dotted line over W1 and label it H1. H1 W1 H T

6. This point of intersection is where the golfer should bank the ball!
5. With a straight edge, connect the tee (T) with H1 to locate where on the wall the ball needs to reflect off of. H1 W1
This point of intersection is where the golfer should bank the ball! H T

7. 6. Draw a line from the point of intersection to H
6. Draw a line from the point of intersection to H. This will complete the path of the ball for getting a hole in one. H1 W1 H T

8. NOTE: The speed of the ball, the type of surface used on the hole, the accuracy of the golfer, and other factors may influence the actual success of the hole-in-one. T

9. Reflections and Geometry Proofs: DOUBLE-BANK
Making the Hole-in-One a Reality

10. 1. Outline a pentomino diagram of your choice.

11. 2. Determine where you want to place the tee (label with a dot and T)
2. Determine where you want to place the tee (label with a dot and T). Determine where you want to place the hole (label with a dot and H). H T

12. 3. Select the TWO walls of the pentomino you will bank the ball off of, starting at the hole and working BACKWARDS. W2
The SECOND wall the ball will hit before entering the hole should be labeled W2. H T

13. 4. The first wall the ball will hit after leaving the tee should be labeled W1.

14. 5. With a compass, construct a dotted line from H that is perpendicular to W2. Reflect this dotted line over W2 and label it H2. H2 W2 H W1 T

15. 6. With a compass, construct a dotted line from H2 that is perpendicular to W1. Reflect this dotted line over W1 and label it H1.
Extension of W1 H1 H2 W2
NOTE: You may have to extend W1 to complete the reflection (see green line). H W1 T

16. 7. With a straight edge, connect the tee (T) with H1.
Extension of W1 H1 H2 W2
This point of intersection is where the golfer should bank the ball! H W1 T

17. 8. Draw a line from the point of intersection on W1 to H2.
Extension of W1 H1 H2 W2
This NEW point of intersection is where the ball will hit W2 (2nd bank). H W1 T

18. 9. Connect this 2nd point of intersection on W2 to H, completing the path of the ball.
Extension of W1 H1 H2 W2
Note: The bold red lines represent the actual path of the ball to achieve a hole in one. H W1 T