Objective: To use properties of perpendicular and angle bisectors.

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Bisectors in Triangles

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Presentation transcript:

Objective: To use properties of perpendicular and angle bisectors. Chapter 5 Lesson 2 Objective: To use properties of perpendicular and angle bisectors.

Perpendicular Bisector Theorem If a point is 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 1: Real-World Connections National Landmarks Find the set of points on the map of Washington, D.C. that are equidistant from the Jefferson Memorial and the White House. The red segment connects the Jefferson Memorial and the White House. All points on the perpendicular bisector m of this segment are equidistant from the Jefferson Memorial and the White House.

Angle Bisector Theorem Converse of the Angle Bisector Theorem If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Theorem 5-5 Converse of the Angle Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

Example 2: Using the Angle Bisector Theorem Find the value of x, then find FD and FB. From the diagram you can see that F is on the bisector of ACE. Therefore, FB = FD.

Example 3: Using the Angle Bisector Theorem According to the diagram, how far is K from ? From ? 10; 10 What can you conclude about ? is the angle bisector of DEH. Find the value of x. 2x=x+20 x=20

Assignment: Page 252 #1-25