5.2. Perpendicular Bisectors in Triangles http://www.ck12.org
Let’s use the Perpendicular Bisector Theorem and its converse in a few examples.
Example 1:Algebra ConnectionFindxand the length of each segment.
Solution:From the markings, we know that
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W Xis the perpendicular bisector ofXY. Therefore, we can use the
Perpendicular Bisector Theorem to conclude thatW Z=WY. Write an equation.
2 x+ 11 = 4 x− 5
16 = 2 x
8 =xTo find the length ofW ZandWY, substitute 8 into either expression, 2( 8 )+ 11 = 16 + 11 =27.
Example 2:
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OQis the perpendicular bisector ofMP.a) Which segments are equal?
b) Findx.
c) IsLon
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OQ? How do you know?Solution:
a)ML=LPbecause they are both 15.
MO=OPbecauseOis the midpoint ofMP
MQ=QPbecauseQis on the perpendicular bisector ofMP.
b) 4x+ 3 = 11
4 x= 8
x= 2
c) Yes,Lis on
←→
OQbecauseML=LP(Perpendicular Bisector Theorem Converse).