6.2 bisectors of a triangle - wordpress.com · 2018-01-06 · nk=2r-2 nl = find nm. a 7 d find nj....

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6.2 Bisectors of a Triangle Perpendicular Bisectors When three or more lines intersect in the same point, they are called concurrent lines. The point of intersection of the lines is called the point on concurrency. In a triangle, the three perpendicular bisectors are concurrent. The point of concurrency is the circumcenter of the triangle. Example 2: Finding the Circumcenter of a Triangle Find the coordinates of the circumcenter of ∆!"# with vertices ! 0,3 , ! 0, −1 , !"# !(6, −1)

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Page 1: 6.2 Bisectors of a Triangle - WordPress.com · 2018-01-06 · NK=2r-2 NL = Find NM. A 7 D Find NJ. 14. NQ=2r NR=3x Find NS. 3 2 In Exercises 5 and 6, the angle bisectors of AXYZ intersect

6.2BisectorsofaTrianglePerpendicularBisectors

Whenthreeormorelinesintersectinthesamepoint,theyarecalledconcurrentlines.Thepointofintersectionofthelinesiscalledthepointonconcurrency.Inatriangle,thethreeperpendicularbisectorsareconcurrent.Thepointofconcurrencyisthecircumcenterofthetriangle.

Example2:FindingtheCircumcenterofaTriangleFindthecoordinatesofthecircumcenterof∆!"#withvertices! 0,3 ,! 0,−1 ,!"# !(6,−1)

Page 2: 6.2 Bisectors of a Triangle - WordPress.com · 2018-01-06 · NK=2r-2 NL = Find NM. A 7 D Find NJ. 14. NQ=2r NR=3x Find NS. 3 2 In Exercises 5 and 6, the angle bisectors of AXYZ intersect

UsingtheIncenterofatriangle Letsbisecteachangle.Thepointofconcurrencyistheincenterofthetriangle.

Example3:UsingtheIncertofatriangleInthefigureshown,!" = 5! − 1and!" = 2! + 11 a)FindNF b)CanNGbeequalto18?Homework3-15odd,29-32,35,36

Page 3: 6.2 Bisectors of a Triangle - WordPress.com · 2018-01-06 · NK=2r-2 NL = Find NM. A 7 D Find NJ. 14. NQ=2r NR=3x Find NS. 3 2 In Exercises 5 and 6, the angle bisectors of AXYZ intersect

Page 4: 6.2 Bisectors of a Triangle - WordPress.com · 2018-01-06 · NK=2r-2 NL = Find NM. A 7 D Find NJ. 14. NQ=2r NR=3x Find NS. 3 2 In Exercises 5 and 6, the angle bisectors of AXYZ intersect

Page 5: 6.2 Bisectors of a Triangle - WordPress.com · 2018-01-06 · NK=2r-2 NL = Find NM. A 7 D Find NJ. 14. NQ=2r NR=3x Find NS. 3 2 In Exercises 5 and 6, the angle bisectors of AXYZ intersect

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