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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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Q: State the Perpendicular Bisector Theorem and its converse as a biconditional?

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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.

Proposition 3 of Book IV in Euclid's Elements (angle bisector 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.

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.

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.

Related questions

The converse of perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Converse of the Perpendicular Bisector Theorem - if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.Example: If DA = DB, then point D lies on the perpendicular bisector of line segment AB.you :))

converse of the perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant, or the same distance, from the endpoints of the segment.

converse of the angle bisector theorem

No, it does not.

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle-apex

The Angle Bisector Theorem states that given triangle and angle bisector AD, where D is on side BC, then . Likewise, the converse is also true. Not sure if this is what you want?

A segment need not be a bisector. No theorem can be used to prove something that may not be true!

a point on the bisector of an angle, it is equidistant from the 2 sides of the angle

No.

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