What kind of Triangle is That

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• What kind of Triangle is That!!

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The Question!!

• What do the relationships between
• The Squares of the Lengths
• Of the sides
• Of different triangles
• Tell us about
• The type of triangle we have?

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Do You remember ???
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The Triangle Inequality!!
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Check this out

• We have 3 side lengths, A, B and C

A
B
C
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Will these sides make a triangle?

• The lengths are A 6 B 11 and C 9

A
B
C
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Hmmmm.

• The lengths are A 6 B 11 and C 9

6
11
6 9 gt 11
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So we do have a triangle.
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Try another combo
In the case of the red figure, the two short
sides, a and b, arent long enough to form a
triangle with side c.
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The Triangle Inequality

• In order for three side lengths to form a
  triangle,
• The sum of the lengths of the two shorter
  sides must be greater than the length of the
  third side.
• ( or they wont reach)

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Why is the Triangle Inequality important when
we are investigating Types of triangles by
evaluating the lengths of their sides?
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Draw this on your graph paper.
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Now add these lines.
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Label the points D, E, F, and G, H, and I Like
this
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If we measure the lengths of the red and blue
lines.
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You get these lengths
AD BD 12.2
AE BE 10.3
AF BF 8.6
AG BG 5.8
AH BH 5.3
AI BI 5.0
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Remember The Question?

• What do the relationships between
• The Squares of the Lengths
• Of the sides
• Of different triangles
• Tell us about
• The type of triangle we have?

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Lets make a table
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Fill in the side
lengths
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Do the CALCULATIONS!!
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Check it out
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What Types
of
TRIANGLES
Did we get??
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ACUTE
OBTUSE
RIGHT
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One Angle must equal 900
RIGHT
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One angle gt 900
OBTUSE
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All angles lt 900
ACUTE
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Check out the triangles
On your graph...
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Are they...
ACUTE
OBTUSE
or
RIGHT
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Fill in your chart!!!
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(No Transcript)
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What did we learn??
(How about another chart??)
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Find one like this and fill it in.
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Some numbers
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More numbers
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Fill in the symbols
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Like this
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Fill in the Type of triangle
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Types of triangles
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Write a Conjecture
About
Types of Triangles
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Is this true??

• If a2 b2 lt c2
• then the triangle is
  Obtuse.
• If a2 b2 gt c2
• then the triangle is
  Acute.
• If a2 b2 c2
• then the triangle is
  Right.

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Eurika!!