Transcript Rewriting Equations & Formulas - Southwest Washington Mathematics

Vertical and Exterior Angle Proofs
The teacher models a proof of the sum of the
angles of a triangle is 180.
In a team of 4, one pair proves the vertical angle
theorem.
The other pair proves the exterior angle
theorem.
Extension: Let students who need a challenge
explore and prove the sum of the exterior
angles of any polygon is 360.
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Vertical and Exterior Angle
Proofs
6/6/14
Southwest Washington Common Core Mathematics
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Practice Target
• Practice 3 Construct viable arguments and
critique the reasoning of others.
• Practice 6. Attend to precision.
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Learning Target
G-COc I can prove geometric theorems.
Prove and apply
• vertical angle theorem
• measures of interior angles of a triangle sum
to 180º
• exterior angles of triangles
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Language
•
•
•
•
•
conjecture
interior angle sum of triangle
interior angle sum of any polygon
vertical angle theorem
exterior angle theorem
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Launch
• What is the value of my coins?”
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Model
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The sum of the angles if a triangle is 180.
I am going to convince
you that the sum of the
angle measures is 180.
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The sum of the angles if a triangle is 180.
• Let’s say m, n and p are
the angle measures.
• What do I need to show
the sum of the
measures of the angles
of a triangle is 180?
• Let’s draw HI parallel to
EG
The sum of the angles if a triangle is 180.
• Since , m = q because
they are alternate
interior angles.
• Also since , p = r
because they are
alternate interior
angles.
The sum of the angles if a triangle is 180.
• Since , m = q because
they are alternate
interior angles.
• Also since , p = r
because they are
alternate interior
angles.
The sum of the angles if a triangle is 180.
• Angle HFI is a straight
angle, so its measure is
180°.
• q + n + r = 180 because
the three measures
make up angle HFI.
• I already showed that m
= q, so I can use
substitution to rewrite
the equation
m + n + r = 180.
The sum of the angles if a triangle is 180.
• Also we know that p = s,
so I can use substitution
to rewrite the equation
again:
m + n + p = 180
• Since this is what I
needed to show, I just
proved that sum of the
angles of a triangle is
180.
Now its your turn!
Each partner in your group will get a different
conjecture.
Convince yourself!
• STEP 1: Prove with a partner.
Convince a friend!
• STEP 2: Compare your proof.
Convince a skeptic!
• STEP 3: Share your proof with your team.
• STEP 4: Write up both proofs.
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• Class presentations!
Now its your turn!
Your group will be split into 2 sets of partners.
You need an individual white board.
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Convince yourself!
STEP 1: Prove with a partner.
• You may want to use some of this evidence in
your proof.
• The sum of the angles of a triangle is 180.
• Supplementary angles add to 180.
• Linear pairs are supplementary.
• The substitution property.
• (Remember the coin example.)
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Convince a friend!
STEP 2:
• Compare your proof to another pair that did
the SAME proof you did.
• You may make changes to your proof.
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Convince a skeptic!
STEP 3:
• Convince the partners at your table of the
validity of your conjecture. After the
presentation, aks questions and give
affirmations to the presenters.
STEP 4:
• Each person on your team needs to write up
and turn in BOTH proofs.
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Debrief
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Language
•
•
•
•
•
conjecture
interior angle sum of triangle
interior angle sum of any polygon
vertical angle theorem
exterior angle theorem
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Learning Target
1
2
3
4
5
Did you hit the target?
G-COc I can prove geometric
theorems.
Prove and apply
• vertical angle theorem
Rate your
• measures of interior angles of
understanding of the
a triangle sum to 180º
target from 1 to 5.
• exterior angles of triangles
5 is a bullseye!
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Practice
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Ticket Out
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