Mini Golf

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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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When this button appears on the lower
right of the screen, you will know it is time to
move to the next slide. Simply click the mouse,
or hit the enter key. If you want to return to a
previous slide, just hit the backspace key.
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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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Hmm.. not exactly as I planned. Ill 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 Id try anything!
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First, lets 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 doesnt work.
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Too bad we cant 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 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 lets label the
reflection of the hole as point H. (H prime)
H
H
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We can also label the intersection of the balls
path and the wall as point W.
H
H
. W
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See what happens when we connect H and H.
H
H
. W
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A right triangle is formed.
H
H
. W
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What would happen if we reflect this triangle
over the wall?
H
H
. W
Lets find out!
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(drum roll, please)
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Its no surprise that the reflected triangle
reveals a path to the hole!
H
H
. W
How, you ask?
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Remember, if two triangles are congruent, then
their corresponding sides and angles are
congruent.
H
H
. W
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The ball is hit towards H. Since it cant go
through the wall, it will reflect off the wall
and travel towards point H.
H
H
. W
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Laurie DiGregorio digregor_at_schools.mtco.com Te
resa Yazujian yazujiant_at_eureka.wodfrd.k12.i
l.us Nancy Powell powelln_at_district87.org