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Triangle Tango
Investigating the Triangle Inequality Theorem
Topics: Triangle
Inequality Theorem,
Triangle Types
Materials List
 6-sided die,
numbered or pip
 12 Drinking straws,
20 cm (8”)
 String, 50 cm
(~20”)
 Scissors
 Rulers
 Data table
Determine if triangles can be formed with side lengths obtained by rolling a die!
To Do and Notice
1. Roll the die three times to determine the side lengths of a triangle. Record in data
table under A, B, and C, respectively.
2. Add side lengths A and B. Record the sum in the data table under A+B.
3. Write an inequality in the table in the format A+B > C, entering the values from
steps 1 and 2 (see example below). Determine if the inequality is true or false.
4. Measure out and cut straw segments (using inches rather than centimeters works
best) according to values from step 1.
5. On a flat surface, lace the string through the straw segments, and then tie the
string ends in overhand fashion, similar to tying a shoelace. Pull slowly to
remove the slack and observe the sides folding up.
6. Are the straw segments touching end-to-end? Is it possible to form a triangle
given the lengths determined by rolling the die? Indicate Yes or No in data table.
7. If a triangle can be formed, indicate the type of triangle from the following:
equilateral (all sides equal), isosceles (two equal sides), scalene (no equal sides).
8. Repeat four more times. Reuse straw pieces when possible.
Trial
This activity can be used
to teach:
Common Core Math
Standards:
 Two Dimensional
shapes (Geometry,
Grade 4, 2; Grade 5,
3-4)
 Angles (Grade 4,
Measurement and
Data, 5, Grade 8,
Geometry, 5)
 Theorems about
triangles (Geometry,
CO.10)
 Problem Solving and
Reasoning
(Mathematical
Practices Grades 4 12)
Ex.
Number Rolled = Side Length (in)
A B C
5 4 4
A+B
5+4=9
A+B > C, True/False?
9 > 4, True
∆ Possible?, Type
Yes, Isosceles
The Math Behind the Activity
One of the most important theorems in Euclidean geometry is the triangle inequality
theorem. This theorem is widely used in architecture and in various engineering
applications. It states that the sum of the lengths of two sides of a triangle is greater
than the length of the third side. Stated another way, the length of one side of a
triangle is less than the sum of the remaining two side lengths.
a
b
For a triangle with sides a, b, & c:
b + c > a or a + c > b or a + b > c
c
Triangles are classified according to their angle and/or side length measures.
Triangles are classified by angle measure as right (one 90° angle), obtuse (one angle
larger than 90°), or acute (all angles < 90°). By side length, triangles are equilateral
(all sides equal), isosceles (two equal sides), or scalene (no equal sides). Side lengths
and angle measures are interrelated, meaning the inequality theorem can be used to
describe the angles as well as the lengths.
Taking it Further

Measure the angles in the formed triangles and note relationships
Web Resources (Visit www.raft.net/raft-idea?isid=611 for more resources!)


Proof - http://www.math.washington.edu/~king/coursedir/m444a03/notes/10-03Triangle-Inequality.html
Teacher designed math courses – https://njctl.org/courses/math
Developed and written by Eric Welker (RAFT)
Copyright 2014, RAFT
Triangle Tango Data Sheet
Trial
Ex.
Number Rolled = Side Length (in)
A B C
5 4 4
A+B
5+4=9
A+B > C, True/False?
9 > 4, True
∆ Possible?, Type
Yes, Isosceles
1
2
3
4
5
Triangle Tango Data Sheet
Trial
Ex.
Number Rolled = Side Length (in)
A B C
5 4 4
A+B
5+4=9
A+B > C, True/False?
9 > 4, True
∆ Possible?, Type
Yes, Isosceles
1
2
3
4
5
Triangle Tango Data Sheet
Trial
Ex.
Number Rolled = Side Length (in)
A B C
5 4 4
A+B
5+4=9
A+B > C, True/False?
9 > 4, True
∆ Possible?, Type
Yes, Isosceles
1
2
3
4
5
Triangle Tango Data Sheet
Trial
Ex.
Number Rolled = Side Length (in)
A B C
5 4 4
A+B
5+4=9
A+B > C, True/False?
9 > 4, True
∆ Possible?, Type
Yes, Isosceles
1
2
3
4
5
Triangle Tango, page 2
Copyright 2014, RAFT