Perpendicular and Angle Bisectors
Perpendicular and Angle Bisectors
G.CO.9 Prove theorems about lines and angles... points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Goals for this section:
Goals for this section:
Students should be able to understand the perpendicular bisector theorem and the angle bisector theorem and how it could be applied to real-life situations.
Perpendicular Bisector Theorem
Perpendicular Bisector Theorem
Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Let's break it down:
Let's break it down:
- Notice the perpendicular bisector forms a right angle (perpendicular) with segment AB.
- Notice the perpendicular bisector splits segment AB into two equal halves (bisects).
- If you pick any point on the perpendicular bisector, A and B will be the same distance away from P (equidistant).
- That is AP ≅ BP.
Extra Property!
Extra Property!
- The angles formed by MAP and MBP are congruent!
- The triangle formed by the dotted lines (APB) is called an isosceles triangle.
Angle Bisector Theorem
Angle Bisector Theorem
Theorem: If a point is on an angle bisector, then the point is equidistant from the sides of the angle.
Theorem: If a point is on an angle bisector, then the point is equidistant from the sides of the angle.
Let's break it down:
Let's break it down:
- An angle bisector divides an angle in two equal halves.
- If you pick any point P on the angle bisector, it will be the same distance away from the sides of the angle (equidistant) when you draw a perpendicular line to the sides.
External Resources
External Resources
Perpendicular Bisector Theorem
Perpendicular Bisector Theorem
Angle Bisector Theorem
Angle Bisector Theorem
Keywords: perpendicular bisector theorem, angle bisector theorem, bisect, perpendicular