A. Answer: No. The Triangle Inequality Theorem is not satisfied
Step-by-step explanation:
Use Pythagorean Theorem or distance formula to find the lengths of each segment.
EF = 3.6 GH = 4.5 IJ = 8.3
The Triangle Inequality Theorem states that the sum of two side lengths must be greater than the length of the third side for ALL sides.
EF + GH > IJ, EF + IJ > GH, and GH + IJ > EF
3.6 + 4.5 > 8.3 3.6 + 8.3 > 4.5 and 4.5 + 8.3 > 3.6
8.1 > 8.3 11.9 > 4.5 and 12.8 > 3.6
FALSE TRUE TRUE
It is not TRUE for all sides so it does not form a triangle!
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B. Answer: No.
The length of one side plus the length of another side must be GREATER than the third side. The given problem uses a "greater than or equal to" sign.
