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## PowerPoint Slideshow about ' Centers of Triangles or Points of Concurrency' - cana

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How many medians does a triangle have?

Three – one from each vertex

The medians of a triangle are concurrent.

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.

2x

x

In ABC, AN, BP, and CM are medians.

If EN = 12, find AN.

C

AE = 2(12)=24

AN = AE + EN

N

P

E

AN = 24 + 12

B

AN = 36

M

A

N

P

E

B

M

A

Example 5

In ABC, AN, BP, and CM are medians.If CM = 24 what is CE?

CE = 2/3CM

CE = 2/3(24)

CE = 16

How many angle bisectors does a triangle have?

three

The angle bisectors of a triangle are ____________.

concurrent

The intersection of the angle bisectors is called the ________.

Incenter

The incenter is the same distance from the sides of the triangle.

Point P is called the __________.

Incenter

How many perpendicular bisectors does a triangle have?

Three

The perpendicular bisectors of a triangle are concurrent.

The intersection of the perpendicular bisectors is called the CIRCUMCENTER.

The Circumcenter is equidistant from the vertices of the triangle.

PA = PB = PC

Example 3: The perpendicular bisectors of triangle ABC meet at point P.

Find DA.DA = 6

BA = 12

- Find BA.

- Find PC.

PC = 10

- Use the Pythagorean Theorem to find DP.

B

6

DP2 + 62 = 102

DP2 + 36 = 100

DP2 = 64

DP = 8

10

D

P

A

C

Tell whether each red segment is an altitude of the triangle.

The altitude is the “true height” of the triangle.

YES

NO

YES

How many altitudes does a triangle have?

Three

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?

NEITHER

ALTITUDE

PER. BISECTOR

BOTH

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