Mini Golf Laurie DiGregorio Germantown Hills Middle School, Metamora, IL 61548 Teresa Yazujian Eureka Middle School, Eureka, IL 61530 Nancy Powell Bloomington High School, Bloomington, IL 61704

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How to Get a Hole - in - one! What a great day for a game of golf! This will be a piece of cake!

It looks like I need to bank this shot… …the trick is to find the right angle.

…not exactly as I planned. Hmm….. …not exactly as I planned. I’ll have to try a new angle.

This could take years before I get it right!

Did you ever think you could use math to get a hole-in-one? At this point… I’d try anything!

First, let’s look at some properties of angles. When the ball hits the wall, it creates an angle of incidence.

As the ball bounces off the wall, an angle of reflection is created.

Something really cool! The angle of incidence and the angle of reflection are ALWAYS congruent.

We know that these angles are congruent because they are reflections of each other. Can our knowledge of reflections help us solve the puzzle?

Remember, we are trying to get a hole-in-one! Since a direct shot is not an option, we will have to bank it off a wall if we want to make a hole-in-one.

We know we want to bank the ball off the left wall of the green.

But how can we use math to determine where the ball should bounce off the wall?

Guess and check sure doesn’t work.

Too bad we can’t just move the flag!

Wait a minute!!!

What if we... MOVED THE FLAG?

But WHERE do we move it???

Think about this: If we move the flag anywhere INSIDE the hole, we have changed the hole… …therefore we have changed the problem. Hint: Think outside the box! Literally!!!

What would that do for us? What if we reflected the hole across the side we want to bank off? What would that do for us?

Do you realize the ball is now in a straight line with the hole? Ok, ok. It is in line with the reflected hole.

Here is the $100,000.00 question of the day: What can a reflection tell us?

If the hole is point H, then let’s label the reflection of the hole as point H’. (H prime)

We can also label the intersection of the ball’s path and the wall as point W.

See what happens when we connect H and H’.

A right triangle is formed. W

What would happen if we reflect this triangle over the wall? . W Let’s find out!

(drum roll, please)

It’s no surprise that the reflected triangle reveals a path to the hole! . W How, you ask?

Remember, if two triangles are congruent, then their corresponding sides and angles are congruent.

The ball is hit towards H’ The ball is hit towards H’. Since it can’t go through the wall, it will reflect off the wall and travel towards point H. H H’ . W

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