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Biconditional Statement for:
Perpendicular Bisector Theorem: A point is equidistant if and only if the point is on the perpendicular bisector of a segment.
Converse of the Perpendicular Bisector Theorem: A point is on the perpendicular bisector of the segment if and only if the point is equidistant from the endpoints of a segment.
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Converse of Pythagorean Theorem?
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
What reasons are proof that the angle bisector construction can be used to bisect any angle?
Proposition 3 of Book IV in Euclid's Elements (angle bisector theorem)
What is the difference between the pythagorean theorem and the converse of the pythagorean theorem?
The Pythagorean Theorem states that in a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. The converse of the Pythagorean theorem states that, if in a triangle with sides a, b, c, a2 + b2 = c2 then the triangle is right and the angle opposite side c is a right angle.
What is the converse of the Hinge Theorem?
Converse of the Hinge Theorem:If tow sides of one triangle are congruent to two sides of another triangle and the the included angles are not congruent, then the included angle that is larger has the longer third side across from it.
Does the pythagorean theorem have a converse?
Yes. If the square of the longest side of a triangle is equal to the sum of the squares on the other two sides, then the triangle is right angled.
