3.6—bisectors of a triangle warm up 1. draw a triangle and construct the bisector of one angle. 2....
TRANSCRIPT
3.6—Bisectors of a Triangle
Warm Up
1. Draw a triangle and construct the bisector of one angle.
2. JK is perpendicular to ML at its midpoint K. List the congruent segments. Draw a picture.
3.6—Bisectors of a Triangle
Objective: Use properties of _____________ bisectors and ___________ bisectors of a __________.
perpendicularangle triangle
Concurrent lines: three or more lines that intersect in the _______ ________
Point of concurrency: the _________ of ________________ of concurrent lines
same point
pointintersection
The circumcenter can be: inside the triangle (acute triangles), on the triangle (right triangles), or outside the triangle (obtuse triangles).
_______________ Bisector of a triangle: a ________ that is perpendicular to a side of the triangle at the __________ of the side.
________________ of a triangle: the point of ____________________ of the perpendicular _______________ of a triangle.
Perpendicularline
midpoint
Circumcenterconcurrency
bisectors
Examples: 1. The perpendicular bisectors of ΔHIJ 2. R is the circumcenter of ΔOPQ, meet at K, IJ = 18, and KJ = 12. OS = 10, QR = 12, and PQ = 22.
a. Find HK. a. Find OP.
b. Find IM. b. Find RP.
c. Find KM. c. Find RT.
________ _____________ of a triangle: a bisector of an _________ of a triangle
_______________ of a triangle:the point of __________________ of the angle bisectors
Angle Bisector angle
Incenterconcurrency
The incenter is always inside the triangle.
Examples: 3. D is the incenter of ΔABC, 4. The angle bisectors of ΔABC meet at P,
a. Find DE. PR = 3 and PC = 5.
b. Find GC. a. Find QP.
b. Find QC.
Construction – Perpendicular to a line from a point not on the line.
Construct a perpendicular to the given line and through the given point.
. A.
B. .
Construct the Circumcenter and the Circumscribed Circle for the triangle.
Construct the Incenter and the Inscribed Circle for the triangle.