1. Triangle Inequality Theorem
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2. Warm Up Give the best name for each quadrilateral. rectangle trapezoid
1) ).
3). 4).
trapezoid
rhombus
parallelogram

3. Triangle Inequality Theorem Exploration
Side Lengths
A + B
<, >, or = C
Triangle?
1, 2, 3
2, 3, 4
1, 3, 5
1, 2, 6
2, 5, 6
3, 4 , 6

4. Triangle Inequality Theorem
Any side of a triangle must be shorter than the other two sides added together. If it was longer, the other two sides would not meet.

5. Example 2: Will the following lengths make a triangle?
5 cm, 7 cm, 4 cm
Example 2: Will the following lengths
make a triangle?
2 in, 4 in, 6 in
5 + 4 = > yes, this makes a triangle
2 + 4 = = no, this does not make a triangle

6. no yes yes yes no yes Practice
Tell if the following side lengths will make a triangle.
1). 7 in, 2 in, 4 in 2). 8 cm, 10 cm, 12 cm
3). 15 yd, 16 yd, 12 yd 4). 7 ft, 8ft, 9 ft
5). 10 in, 12 in, 22 in 6). 5 cm, 8 cm, 4 cm no
yes
yes
yes no
yes

7. Closure
What are the possible lengths for the third side of a triangle with the following 2 lengths? in and 4 in
2, 3, 4, 5,
6,7,8