Theorems 4-5/4-6 and 4-7/4-8

Question 1

Theorem 4-5

Answer 1

If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

Question 2

Theorem 4-6

Answer 2

If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

CONVERSE of Theorem 4-5

Question 3

What is the biconditional statement for Theorem 4-5 and 4-6?

Answer 3

A point is on the perpendicular bisector of a segment if and only if it equidistant from the endpoint of the segment.

Question 4

Theorem 4-7

Answer 4

If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.

Question 5

Theorem 4-8

Answer 5

If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

Question 6

What is the biconditional statement for Theorem 4-6 and 4-7?

Answer 6

A point is on the bisector of an angle if and only if it is equidistant from the sides of the angle.