5.2. Perpendicular Bisectors http://www.ck12.org
Practice
1.mis the perpendicular bisector ofAB.
a. List all the congruent segments.
b. IsConAB? Why or why not?
c. IsDonAB? Why or why not?For Question 2, determine if
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STis the perpendicular bisector ofXY. Explain why or why not.2.For Questions 3-7, consider line segmentABwith endpointsA( 2 , 1 )andB( 6 , 3 ).
- Find the slope ofAB.
- Find the midpoint ofAB.
- Find the equation of the perpendicular bisector ofAB.
- FindAB. Simplify the radical, if needed.
- PlotA,B, and the perpendicular bisector. Label itm. How could you find a pointConm, such thatCwould
be the third vertex of equilateral triangle 4 ABC?You do not have to find the coordinates, just describehow
you would do it.
For Questions 8-12, consider 4 ABCwith verticesA( 7 , 6 ),B( 7 ,− 2 )andC( 0 , 5 ). Plot this triangle on graph paper.
- Find the midpoint and slope ofABand use them to draw the perpendicular bisector ofAB. You do not need to
write the equation. - Find the midpoint and slope ofBCand use them to draw the perpendicular bisector ofBC. You do not need to
write the equation. - Find the midpoint and slope ofACand use them to draw the perpendicular bisector ofAC. You do not need to
write the equation. - Are the three lines concurrent? What are the coordinates of their point of intersection (what is the circumcenter
of the triangle)? - Use your compass to draw the circumscribed circle about the triangle with your point found in question 11 as
the center of your circle. - Fill in the blanks: There is exactly _____ circle which contains any __ points.
- Fill in the blanks of the proof of the Perpendicular Bisector Theorem.
Given:
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CDis the perpendicular bisector ofABProve:AC∼=CB
TABLE5.2:
Statement Reason
1.
2.Dis the midpoint ofAB- Definition of a midpoint
4.^6 CDAand^6 CDBare right angles
5.^6 CDA∼=^6 CDB - Reflexive PoC
- 4 CDA∼= 4 CDB
8.AC∼=CB