Name:
Date: _____________________
PMI – 7th Grade Math – Triangle Inequality Lab
Supplies:
 Scissors
 Pencil
 Ruler
Task #1: Cut on each set of dotted lines (
--------) for the segments that will be used to
assemble each triangle. Place each set of segments off to the side.
Task #2: Examining each set of segments
1. Cut out each segment in set A
2. Measure the length of each segment. Record your answers in labeled columns
(Small, Medium & Large) of the table below. Round your answers to the nearest
tenth of a centimeter.
3. Fill in column #4 (Small + Medium) of the table below.
4. Try to arrange the segments so that a triangle (∆) is created.
a. If so, write “Yes” in column #5 (Can it make a ∆?)
b. If not, write “No” in column #5
5. Repeat steps #1-4 for the segments in set B, C, D, E, and F
Segment
Set
Small
Medium
Large
Small +
Medium
Can it make
a ∆?
A
B
C
D
E
F
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Questions:
1. Based on your observations, write a conjecture about the relationship between the
small and medium sides of a triangle and the measure of the larger side of the
triangle. Explain how you came up with your conjecture.
2. Is it possible to have a triangle such that the sum of the measures of the small and
medium sides is equal to the measure of the large side? Explain how you came up
with your answer (You may use one of the segment lengths from above, if you would
like).
3. If the sum of the measures of the small and medium sides of a triangle is greater
than the measure of the large side of the triangle, we can conclude that the sum of
the measures of any other pair of sides of the triangle will be greater than the
measure of the remaining side. Explain why this conclusion is possible.
4. In the box below, write three inequalities that are always true for a triangle with
side lengths a, b, and c (instead of s, m, and l for small, medium, and large).
TRIANGLE INEQUALITY
In a triangle with side lengths a, b, and c
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+
>
+
>
+
>
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Segment Set A:
A
A
A
--------------------------------------------------------------------------------------------------------------------Segment Set B:
B
B
B
--------------------------------------------------------------------------------------------------------------------Segment Set C:
C
C
C
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Segment Set D:
D
D
D
--------------------------------------------------------------------------------------------------------------------Segment Set E:
E
E
E
--------------------------------------------------------------------------------------------------------------------Segment Set F:
F
F
F
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Name:
KEY
Date: _____________________
PMI – 7th Grade Math – Triangle Inequality Lab
Segment
Set
Small
Medium
Large
Small +
Medium
Can it make a
∆?
A
4 cm
6 cm
9.5 cm
10 cm
Yes
B
5 cm
6 cm
13 cm
11 cm
No
C
5.3 cm
7 cm
8.5 cm
12.3 cm
Yes
D
3.5 cm
6.5 cm
10 cm
10 cm
No
E
5.3 cm
5.3 cm
7.5 cm
10.6 cm
Yes
F
6 cm
7 cm
13 cm
13cm
No
1. The small side & medium side must add up to be greater than the large side in order
to make a triangle.
2. No. When the small side and medium side added up to be equal to the large side, it
formed a straight line, not a triangle.
3. If you add up the large side and the small side, it has to be greater than the medium
side.
If you add up the large side and the medium side, it has to be greater than the small
side.
4.
TRIANGLE INEQUALITY
In a triangle with side lengths a, b, and c
a
+
b
>
c
a
+
c
>
b
b
+
c
>
a
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