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Published byNicole Graves Modified over 4 years ago

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

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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!

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**It looks like I need to bank this shot…**

…the trick is to find the right angle.

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**…not exactly as I planned.**

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

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**This could take years before I get it right!**

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**Did you ever think you could use math to get a hole-in-one?**

At this point… I’d try anything!

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**First, let’s look at some properties of angles.**

When the ball hits the wall, it creates an angle of incidence.

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

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**Something really cool! The angle of incidence and the**

angle of reflection are ALWAYS congruent.

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**We know that these angles are congruent because they are reflections of each other.**

Can our knowledge of reflections help us solve the puzzle?

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**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.

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

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

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**Guess and check sure doesn’t work.**

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**Too bad we can’t just move the flag!**

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Wait a minute!!!

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What if we... MOVED THE FLAG?

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But WHERE do we move it???

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**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!!!

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**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?

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**Do you realize the ball is now in a straight line with the hole?**

Ok, ok. It is in line with the reflected hole.

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**Here is the $100,000.00 question of the day:**

What can a reflection tell us?

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

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

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**See what happens when we connect H and H’.**

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**A right triangle is formed.**

W

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**What would happen if we reflect this triangle over the wall?**

. W Let’s find out!

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(drum roll, please)

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**It’s no surprise that the reflected triangle reveals a path to the hole!**

. W How, you ask?

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

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**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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**The End! 31 Online Mini Golf Games - http://www.thepinballzone.net/**

Want to play mini-golf online? 31 Online Mini Golf Games -

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When figures have the same size and shape we say they are congruent. In this lesson I will focus on congruent triangles.

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