Download Possible Triangle Constructions

Possible Triangle Constructions
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Projector Resources
Possible Triangle Constructions
• What facts do you know about triangles?
• What names do you know for different types
of triangles?
• How do we label sides and angles if they are
equal in magnitude?
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Possible Triangle Constructions
P-1
Triangles
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Possible Triangle Constructions
P-2
• The sum of the interior angles of all triangles
is 180 ⁰.
• Triangles can be equilateral, isosceles, scalene, right
angled, acute, obtuse… …
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Possible Triangle Constructions
P-3
Possible Triangle ABC?
We know the length of two sides and one
angle. Is it possible to construct a triangle with
these properties? If yes, please create a
sketch. If no, please explain why.
AB = 4cm,
AC = 4cm,
Angle B = 40°.
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Possible Triangle Constructions
P-4
• Use mathematical reasoning to determine
whether or not the information given
describes a possible triangle.
• Think carefully about any sketches you may
draw and what your sketch can tell you about
a possible triangle construction.
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Possible Triangle Constructions
P-5
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Possible Triangle Constructions
P-6
• With your group, divide your posters into
three columns and label them ‘Unique,’ ‘More
than One,’ and ‘Not Possible.’
• For each of the cards, you and your partner
need to decide whether from the information
given; a unique triangle can be drawn, more
than one triangle can be drawn, or no
triangles are possible.
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Possible Triangle Constructions
P-7
Working Together
1. Take turns to select any card.
2. Work individually: can a triangle be produced?
3. Decide together how many triangles are possible (one, more
than one, none).
• If a triangle is not possible, agree on your reasoning.
• If you disagree, challenge each other’s explanations and work
together to resolve your disagreements.
4. Once agreed, glue the card in the appropriate column and
write an explanation in pencil on your poster, before moving
on to another card.
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Possible Triangle Constructions
P-8
Think About… …
• How do the given side lengths relate to each
other?
• Is there any information you have not been
given that you need or could work out?
What does this tell you about the number of
possible triangles?
• Why can you draw more than one triangle for
one card, but not another card?
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Possible Triangle Constructions
P-9
Sharing Work
1. Select a card that describes a unique triangle.
Defend your reasoning why it is a unique triangle.
2. Selecta card that describes more than one possible
triangle. Defend your reasoning why this is so.
3. Select a card that does not describe a possible
triangle. Defend your reasoning.
4. Do any groups disagree with any of these
discussions? Defend your reasoning.
5. Which card did you find most difficult to categorize?
Why?
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Possible Triangle Constructions
P-10
Choose Some Measures
• Suggest some measurements for angles A
and B that would make triangle ABC a
possible triangle.
• How many possible triangles do these
measurements make?
• Can you suggest measurements that would
make the triangle unique? How about
impossible? Angle A = ….. ,
Angle B = ….. ,
Angle C = 50°.
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Possible Triangle Constructions
P-11
Choose Some Measures
• Suggest some measurements for sides AB
and AC that would make triangle ABC a
possible triangle.
• How many possible triangles do these
measurements make?
• Can you suggest measurements that would
make the triangle impossible?
BC = 4cm ,
AB = ….. ,
AC = ….. .
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Possible Triangle Constructions
P-12