section 5.3: bisectors in triangles · 2017. 11. 8. · section 5.3: bisectors in triangles...
TRANSCRIPT
Section 5.3: Bisectors in Triangles
when three or more lines intersect at one point
when the circumcenter is used as the center of a circle that contains each vertex of a triangle
the point at which concurrent lines intersect
point of concurrency of the perpendicular bisectors of a triangle
when the incenter is used as the center of a circle that contains exactly one point of each side of a triangle
point of concurrency of the angle bisectors of atriangle
Section 5.3: Bisectors in TrianglesObjective: To identify properties of perpendicular bisectors and angle bisectors
Example 1: Finding the Circumcenter of a TriangleWhat is the center of the circle that you can circumscribe about a triangle with vertices A(3, 5), B(0, 0) and C(8, 0)?
Quick Check:
What are the coordinates of the circumcenter for the triangle with vertices A(2,7), B(10,7), and C(10,3)?
0°118
0°104
Section 5.3: Bisectors in TrianglesObjective: To identify properties of perpendicular bisectors and angle bisectors
Example 2: Using a CircumcenterA civil engineer wants to install a cell phone tower that is equidistant from the mall, the airport, and the subway. How should the civil engineer determine where to build the tower?
Quick Check:
A town planner wants to place a bench equidistant from the three trees in the park. Where should they place the bench?
0°72
0°118
Section 5.3: Bisectors in TrianglesObjective: To identify properties of perpendicular bisectors and angle bisectors
Example 3: Identifying and Using the Incenter of a TriangleGB = 8x - 7 and GD = 5x + 8. What is GF?
Quick Check:
QN = 5x + 36 and QM = 2x + 51. What is QO?
Is it possible for QP to equal 50? Explain.
A
B
C D E
FG
K
NP
LMJ
O
Q
Incenter
0°
48