Centers of Triangles or Points of Concurrency. Medians. Median. vertex to midpoint. Example 1. M. D. P. C. What is NC if NP = 18?. MC bisects NP…so 18/2. 9. N. If DP = 7.5, find MP. 15. 7.5 + 7.5 =. How many medians does a triangle have?. Three – one from each vertex.
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vertex to midpoint
What is NC if NP = 18?
MC bisects NP…so 18/2
If DP = 7.5, find MP.
7.5 + 7.5 =
Three – one from each vertex
The intersection of the medians is called the CENTRIOD.
They meet in a single point.
The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.
vertex to side cutting angle in half
5(x – 1) = 4x + 1
5x – 5 = 4x + 1
x = 6
The angle bisectors of a triangle are ____________.
The intersection of the angle bisectors is called the ________.
Point P is called the __________.
midpoint and perpendicular
(don't care about no vertex)
Example 1: Tell whether each red segment is a perpendicular bisector of the triangle.
3x + 4
5x - 10
x = 7
The perpendicular bisectors of a triangle are concurrent.
The intersection of the perpendicular bisectors is called the CIRCUMCENTER.
PA = PB = PC
DA = 6
BA = 12
PC = 10
DP2 + 62 = 102
DP2 + 36 = 100
DP2 = 64
DP = 8
vertex to opposite side and perpendicular
The altitude is the “true height” of the triangle.
The altitudes of a triangle are concurrent.
The intersection of the altitudes is called the ORTHOCENTER.
Tell if the red segment is an altitude, perpendicular bisector, both, or neither?