Determining if a Triangle is Possible

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Determining if a Triangle is Possible
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How many different acute triangles can you
draw? How many different right scalene triangles
can you draw? Recall that triangles can be
classified according to their side lengths and
the measure of their angles. Sides Scalene - no
sides are congruent Isosceles - two sides are
congruent Equilateral - all three sides are
congruent Angles Acute - all three angles are
acute Right - contains one right angle Obtuse -
contains one obtuse angle
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There is another property that applies to
triangles The sum of the lengths of any two
sides of a triangle is greater than the length of
the third side. What does this mean? If you
take the three sides of a triangle and add them
in pairs, the sum is greater than (not equal to)
the third side. If that is not true, then it is
not possible to construct a triangle with the
given side lengths.
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Example Determine if sides of length 5 cm, 8 cm
and 12 cm can form a triangle? Test all three
pairs to see if the sum is greater 5 8 gt 12 5
12 gt 8 8 12 gt 5 13 gt 12 17 gt 8 20
gt 5 Yes, it is possible to construct a triangle
with sides of lengths 5 cm, 8 cm and 12 cm.
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Example Determine if sides of length 3 ft, 4 ft
and 9 ft can form a triangle? Test all three
pairs to see if the sum is greater 3 4 gt 9 3
9 gt 4 4 9 gt 3 7 gt 9 12 gt 4 13 gt
3 No, it is not possible to construct a triangle
with sides of lengths 3 ft, 4 ft and 9 ft.
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Try These Determine if triangles can be formed
with the following side lengths 1. 4 cm, 7 cm,
10 cm 2. 24 mm, 20 mm, 30 mm 4 7 gt 10
24 20 gt 30 4 10 gt 7
24 30 gt 20 7 10 gt 4
20 30 gt 24 YES
YES 3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24
in 7 9 16 9 13 lt 24 7 16
gt 9 9 24 gt 13 16 9 gt 7
13 24 gt 9 NO NO
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1
Determine if sides of length 5 mm, 14 mm and 19
mm can form a triangle. Be prepared to show your
work!
A Yes
B No
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2
Determine if sides of length 6 in, 9 in and 14 in
can form a triangle. Be prepared to show your
work!
A Yes
B No
9
3
Determine if sides of length 5 yd, 13 yd and 21
yd can form a triangle. Be prepared to show your
work!
A Yes
B No
10
4
Determine if sides of length 3 ft, 8 ft and 15
ft can form a triangle. Be prepared to show your
work!
A Yes
B No
11
5
Determine if sides of length 5 in, 5 in and 9 in
can form a triangle. Be prepared to show your
work!
A Yes
B No
12
6
A triangle could have which of the following sets
of angles?
A
B
C
D
13
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A triangle could have which of the following sets
of angles?
A
B
C
D
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Example Predict the length of the third side of
a triangle with sides of length 12 ft and 16
ft. Side 1 12 ft Side 2 16 ft The 3rd side
must be less than 12 16 gt 3rd side 28
ft gt 3rd side The 3rd side must be greater
than 12 3rd side gt 16 3rd side gt 4 The 3rd
side must be greater than 4 ft and less than 28
ft.
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Example Predict the length of the third side of
a triangle with sides of length 9 cm and 15
cm. Side 1 9 cm Side 2 15 cm The 3rd side
must be less than 9 15 gt 3rd side 24 cm gt
3rd side The 3rd side must be greater than 9
3rd side gt 15 3rd side gt 6 The 3rd side
must be greater than 6 cm and less than 24 cm.
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Try These Predict the length of the third side
of a triangle whose known sides are lengths 1.
13 mm, 20 mm 2. 7 in, 19 in 13 20 gt Side
3 7 19 gt Side 3 33 gt Side 3
26 gt Side 3 13 Side 3 gt 20 7
Side 3 gt 19 Side 3 gt 7 Side 3
gt 12 7 lt side 3 lt 33 12 lt side 3 lt 26
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Try These Predict the length of the third side
of a triangle whose known sides are lengths 3.
4 ft, 11 ft 4. 23 cm, 34 cm 4
11 gt Side 3 23 34 gt Side 3 15 gt Side 3
57 gt Side 3 4 Side 3 gt 11 23
Side 3 gt 34 Side 3 gt 7
Side 3 gt 11 7 lt side 3 lt 15 11 lt side
3 lt 57
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8
Predict the lower limit of the length of the
third side of a triangle whose known sides are
lengths 6 m and 12 m.
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Predict the upper limit of the length of the
third side of a triangle whose known sides are
lengths 6 m and 12 m.
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10
Predict the lower limit of the length of the
third side of a triangle whose known sides are
lengths 9 in and 17 in.
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Predict the upper limit of the length of the
third side of a triangle whose known sides are
lengths 9 in and 17 in.
22
12
Predict the lower limit of the length of the
third side of a triangle whose known sides are
lengths 15 ft and 43 ft.
23
13
Predict the upper limit of the length of the
third side of a triangle whose known sides are
lengths 15 ft and 43 ft.