Brain Brain StrainStrain

Find the value of x.

x x x

xx

Special Special Segments in Segments in

TrianglesTriangles

Median

MedianMedian

Altitude

AltitudeAltitude

Tell whether each red segment is an altitude of the triangle.The altitude is the “true height” of

the triangle.

Perpendicular Bisector

Perpendicular Perpendicular BisectorBisector

Tell whether each red segment is an perpendicular bisector of the triangle.

Angle Bisector

Angle BisectorAngle Bisector

Drill & Drill & PracticePractice

Indicate which special triangle segment the red line is based on the picture and markings

20 20

Points of Points of ConcurrencyConcurrency

The intersection of the angle bisectors is called the INCENTER.

Equidistant to the sides

The intersection

of the altitudes is called the

ORTHOCENTER.

The intersection

of the medians is called the CENTROID.

Vertex to Centroid is Twice as Long as Centroid to Midpoint

The intersection

of the perpendicular

bisector is called the

CIRCUMCENTER.

Equidistant to the vertices

Memorize these!Memorize these!

MCAOABI

PBCC

Medians/Centroid

Altitudes/Orthocenter

Angle Bisectors/Incenter

Perpendicular Bisectors/Circumcenter

Will this work?Will this work?

MCAOABI

PBCC

My Cat

Ate Our

Apples But I

Prefer Blue Cheese Crumbles

Special Property Special Property of Mediansof Medians

Theorem

Vertex to CENTROID is

TWICE as long as CENTROID to

MIDPOINT

vertex

centroid

midpoint

A BF

X

E

C

D

A BF

X

E

C

D

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

A

BM

P E

C

N

If EM = 3, find EC.

Ex: 1

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

A

BM

P E

C

N

If EN = 12, find AN.

Ex: 2

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

A

B

M

P E

C

N

If CM = 3x + 6, and CE = x + 12, what is x?

CM = CE + EM

Ex: 3