# Summarize by liaoqinmei

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```									           Proof:
Meaningful and as a Problem-
• First, inductive approach to find a
pattern, make a conjecture
• Then prove deductively
• Then explain, discuss, compare,
analyze, evaluate
Fido Problem and Proof
Launch
Fido guards a yard. Put Fido on a leash and
secure the leash in the yard so that all of the
yard is guarded and the shortest possible
leash used.
•   Can you find a solution if the yard is shaped
like a circle? If so, what is the solution?
•   How about if the yard is square-shaped?
•   Other shapes?
•   Now think about a triangular-shaped yard …
The Problem
A yard is shaped like a right triangle.
Fido will be on a leash and will guard the
yard.
Put Fido on a leash and secure the leash
somewhere in the yard.
Make sure Fido can reach every corner of
the yard.
Use the shortest leash possible.
Where should you secure the leash?
What we did previously
(or do it now)
Work collaboratively on this problem.
Propose a solution.
Make a conjecture for a mathematical
theorem.
(Today we will prove, in several ways.)
What we did previously
(or do it now)
• What is the solution to the problem?
(See GSP sketch.)
• What is the geometry theorem?
(See next slide.)
Fido Conjecture
The midpoint of the hypotenuse of a
right triangle is equidistant from the
three vertices of a triangle.
Explore
• Examine the 4 diagrams (attached).
• Write a complete proof associated with
each diagram.
• Put one proof on chart paper and be
prepared to present and explain.
Summarize
Present & explain proofs. Discuss the following:
• Describe the general strategy in each proof.
of each general method of proof?
• How are the strategies and proofs similar and
different?
• Are some proofs easier or more convincing to
you than others? Why?
• What mathematical ideas are used in these
proofs?
Fido Proof: lesson format
• Launch – Recall and discuss Fido problem
(or do it now), state the conjecture
• Explore – Do and explain 4 proofs, in groups
• Summarize – Groups present, discuss
summary questions
• Modify/Extend – locus problem, PSSM p.
358
• Check for Understanding – Teacher task:
How and what would you assess?
Proof:
Meaningful and as a Problem-