The Converse of the Pythagorean Theorem. Geometry. Using the Converse. The Converse of the Pythagorean Theorem is True. Remember “Converse” means “Reverse.”.
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If c2 = a2 + b2, then ∆ABC is a right triangle.Theorem 9.5: Converse of the Pythagorean Theorem
The triangle is a right triangle.
The triangle is NOT a right triangle.
If c2 < a2 + b2, then ∆ABC is acuteTheorem 9.6—Triangle Inequality
c2 < a2 + b2
If c2 > a2 + b2, then ∆ABC is obtuseTheorem 9.7—Triangle Inequality
c2 > a2 + b2
A friend measures the four sides to be 30 feet, 30 feet, 72 feet, and 72 feet. He says these measurements prove that the foundation is rectangular. Is he correct?Ex. 3: Building a foundation
b. You measure one of the diagonals to be 78 feet. Explain how you can use this measurement to tell whether the foundation will be rectangular.
Because 302 + 722 = 782, you can conclude that both the triangles are right triangles. The foundation is a parallelogram with two right angles, which implies that it is rectangularEx. 3: Building a foundation