http://www.ck12.org Chapter 5. Relationships with Triangles
15.
For Questions 16-20, 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 21-25, 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 24 as
the center of your circle. - Repeat questions 21-25 with 4 LMOwhereL( 2 , 9 ),M( 3 , 0 )andO(− 7 , 0 ).
- Repeat questions 21-25 with 4 REXwhereR( 4 , 2 ),E( 6 , 0 )andX( 0 , 0 ).
- Can you explain why the perpendicular bisectors of the sides of a triangle would all pass through the center
of the circle containing the vertices of the triangle? Think about the definition of a circle: The set of all point
equidistant from a given center. - 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:←→
CDis the perpendicular bisector ofABProve:AC∼=CBTABLE5.2:
Statement Reason
1.