What is a locus? What is the relationship between a perpendicular bisector of a segment and the segment’s endpoints? What is the relationship between the.

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Presentation transcript:

What is a locus? What is the relationship between a perpendicular bisector of a segment and the segment’s endpoints? What is the relationship between the points on an angle bisector and the angle sides? Perpendiculars, Bisectors and Locus 4-3C

Definition A locus is the set of all the points that satisfy a given condition.

Determine the locus of points in a plane 1 in. from a given point Q. Q What do you get?

Try It Describe the locus of points in space that are 2 in. from a given point C.

Build it there… You will need a piece of paper, a rule, and a protractor. Turn to page 300 in your book.

Perpendicular Bisector A perpendicular bisector of a segment is a line, ray, segment or plane this is perpendicular to the segment and divides it into two congruent segments. AB C m

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

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

What is a locus? A locus is the set of all the points that satisfy a given condition. What is the relationship between a perpendicular bisector of a segment and the segment’s endpoints? The points on the perpendicular bisector of a segment are equidistant from the segment’s endpoints. What is the relationship between the points on an angle bisector and the angle sides? The points on an angle bisector are equidistant from the angle sides.

Assignment 4-3C Page 301, 1-4, 7, 8, 12