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Section 5 – 2 Bisectors in Triangles. Objective: To use properties of perpendicular and angle bisectors. Theorem 5 – 2 Perpendicular Bisector Theorem. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
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Section 5 – 2Bisectors in Triangles Objective: To use properties of perpendicular and angle bisectors.
Theorem 5 – 2Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Theorem 5 – 3Converse 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 Using The Perpendicular Bisector Theorem A) Use the information in the diagram to find CA and DB. Explain your reasoning.
B) Use the diagram to answer each of the following: 1) 2) 3) 4) 5)
C) Use the diagram to answer each of the following: 1) 2) 3)
The Distance From A Point To A Line: The length of the perpendicular segment from the point to the line.
Theorem 5 – 4Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Theorem 5 – 4Converse 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 A) Use the information in the diagram to find the value of x, then find FD and FB. Explain your reasoning.
B) Use the diagram to answer each of the following: 1) How far is K from 2) How far is K from 3) What can you conclude about 4) Find the value of x. 5) Find m ∠DEH.
C) Use the diagram to answer each of the following: 1) Find the value of x. 2) Find CG. 3) Find the perimeter of quadrilateral ABCG.
