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A Perpendicular Proof
Is Every point on the perpendicular bisector of a line segment equidistant from the two endpoints of the segment? Remember your answer from last homework? Well, all those locations can be connected to form a line. Did you notice that the line is perpendicular to the line-segment connecting both flowers? 
 
 Wait!
That means that ANY perpendicular
line will show you the perfect location for the sprinkler so that the sprinkler
can provide the SAME amount of water to each flower?
NO WAY!
There is ONLY one . The one that
goes right through the middle of the line segment connecting both flowers! We
call that point: The Midpoint.
Go ahead and take another look
to the diagram from your last homework and compare it to the one on this
classwork.
Do they look similar?
Well done!
Now you are about to prove something.
Proving something is a little be different than solving a problem.
You will need to think in term
of facts that you know and can prove.
 To
Understand the following you must have your book with you.
If you don't have it, stop.
Go and get your textbook. I will be
here waiting.
Ok, now that you have your book
open on page 72, look at the diagram again.
Let's make a list of things that you know.
1. The diagram is showing 2 right
triangles. The triangle ADC and the triangle _____.
How do you know that they are right
triangles? (Hint: Perpendicular)
Because
..._______________________________________________________
2. Which side is common to both
right triangles? ______
3. How are the lengths of CA and CB in
relation to each other?
How do you know? (Hint: Midpoint)
Base on facts 1, 2, and 3 can
you prove that the two right triangles are congruent?
Do you already know what congruent
means?
Question:
What rule or theorem will you used
if you know two sides of a right triangle and want to find the missing side?
(Hint: legs, square and more square)
_______________________________________________________________
Well go ahead and apply that
theorem to prove that the two missing sides are equal.
Don't forget to mention that
the two triangle are congruent because their sides and they angles are
equal.
Extra points
What are the minimal
conditions needed to be certain that two triangle are congruent?
________________________________________________________________
Please let me know.
To finish, make sure that your
work has the following 4 parts:
A diagram (copy the
diagram from your book.)
A hypothesis (what you
are about to prove.)
Your work (all your
calculations.)
Your Conclusion.
Mr. Lora
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