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
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.
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 > 12
5 + 12 > 8
8 + 12 > 5
13 > 12
17 > 8
20 > 5
Yes, it is possible to construct a triangle with sides of
lengths 5 cm, 8 cm and 12 cm.
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>9
3+9>4
4+9>3
7>9
12 > 4
13 > 3
No, it is not possible to construct a triangle with sides of
lengths 3 ft, 4 ft and 9 ft.
Try These:
Determine if triangles can be formed with the following side
lengths:
1. 4 cm, 7 cm, 10 cm
4 + 7 > 10
4 + 10 > 7
7 + 10 > 4
YES
2. 24 mm, 20 mm, 30 mm
24 + 20 > 30
24 + 30 > 20
20 + 30 > 24
YES
3. 7 ft, 9 ft, 16 ft
4. 9 in, 13 in, 24 in
7 + 9 = 16
7 + 16 > 9
16 + 9 > 7
NO
9 + 13 < 24
9 + 24 > 13
13 + 24 > 9
NO
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
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
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
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
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
6
A triangle could have which of the following
sets of angles?
A
B
C
D
7
A triangle could have which of the following
sets of angles?
A
B
C
D
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 > 3rd side
28 ft > 3rd side
The 3rd side must be greater than:
12 + 3rd side > 16
3rd side > 4
The 3rd side must be greater than 4 ft and less than 28 ft.
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 > 3rd side
24 cm > 3rd side
The 3rd side must be greater than:
9 + 3rd side > 15
3rd side > 6
The 3rd side must be greater than 6 cm and less than 24 cm.
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 > Side 3
33 > Side 3
7 + 19 > Side 3
26 > Side 3
13 + Side 3 > 20
Side 3 > 7
7 + Side 3 > 19
Side 3 > 12
7 < side 3 < 33
12 < side 3 < 26
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 > Side 3
15 > Side 3
23 + 34 > Side 3
57 > Side 3
4 + Side 3 > 11
Side 3 > 7
23 + Side 3 > 34
Side 3 > 11
7 < side 3 < 15
11 < side 3 < 57
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.
9
Predict the upper limit of the length of the
third side of a triangle whose known sides
are lengths 6 m and 12 m.
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.
11
Predict the upper limit of the length of the
third side of a triangle whose known sides
are lengths 9 in and 17 in.
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.
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.