Special Segments in Triangles

Surrrre they are…

There are 4 specialThere are 4 special segments in a triangle.segments in a triangle.

When all the segments of a typeWhen all the segments of a typeare drawn, they are concurrentare drawn, they are concurrent(intersect at the same point).(intersect at the same point).

The points have special names and The points have special names and special properties.special properties.

DON’T DON’T COPY!!!COPY!!!

Start at a vertex and form a Start at a vertex and form a 9090° angle° anglewith the line containing the opposite side.with the line containing the opposite side.

OrthocenterOrthocenter

The The orthocenterorthocenter can be located can be locatedin the triangle, on the triangle orin the triangle, on the triangle oroutside the triangle.outside the triangle.

RightRight

Legs are altitudesLegs are altitudes

ObtuseObtuse

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orthocenterorthocenter CLICK HERE

Angle bisectors start at a vertexAngle bisectors start at a vertexand and bisect the angle.bisect the angle.

IncenterIncenter

TheThe Incenter Incenter is equidistance is equidistance from all 3 sidesfrom all 3 sides

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Incenter

CLICK HERECLICK HERE

A Perpendicular bisector of a side A Perpendicular bisector of a side does notdoes not have to start at a vertex. It will formhave to start at a vertex. It will form a a 9090° angles° angles and bisectand bisect the side. the side.

CircumcenterCircumcenter

#3#3

This makes the This makes the CircumcenterCircumcenter an anequidistance from the 3 verticesequidistance from the 3 vertices

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CircumcenterCircumcenter

The median starts at a vertex and endsThe median starts at a vertex and endsat the at the midpointmidpoint of the opposite side. of the opposite side.

CentroidCentroid

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CentroidCentroid

Altitude ..Altitude .. Vertex .. 90Vertex .. 90°° .. .. OrthocenterOrthocenter

Angle BisectorAngle Bisector.... Vertex…split angles .. Vertex…split angles .. IncenterIncenterPerpendicular BisectorPerpendicular Bisector……

90° .. bisects side .. 90° .. bisects side .. CircumcenterCircumcenterMedianMedian .. ..

Vertex .. Midpoint of side ..Vertex .. Midpoint of side ..CentroidCentroid

Give the best name for ABGive the best name for ABAA

BB

AA

BB

AA

BB

AA

BB

AA

BB||||

|| ||

||||

MedianMedian PerpPerp BisectorBisector

AltitudeAltitude NoneNone

Angle Bisector Angle Bisector

Triangle Activity in Plastic Sleeve

• 1

PP

QQDD

• 2

PPQQ

DD

• 3 PP DD

QQ

• 4PP

QQDD

Back to Notes• Special Fact: segment drawn from

midpoint to midpoint is half the measure of the parallel side

16 m16 m

8 m8 m

X - 3X - 3

2424

The The centroidcentroid is 2/3’s of the distance is 2/3’s of the distance from the vertex to the side.from the vertex to the side.

2x2x

xx

1010

55

3232

XX1616

If AB = 24, AE = 30, and DZ = 16, find AZ, ZB, AC, CE, EZ, and ED.

AA

BB

CC DD

EE FF

ZZ

The The centroidcentroid is the center of balance is the center of balance for the triangle. You canfor the triangle. You can

balance a triangle on the tip ofbalance a triangle on the tip ofyour pencil if you place the tip onyour pencil if you place the tip on

the the centroidcentroid

ELM

ELM

POSTPOST

Angle bisector for the streetsAngle bisector for the streetsPerpendicular bisector for housesPerpendicular bisector for houses

Where would you place a fire hydrant toWhere would you place a fire hydrant tomake it equidistance to the houses make it equidistance to the houses andand

equidistance to the streets?equidistance to the streets?

ELM

ELM

POSTPOST

Survival TrainingSurvival TrainingYou’re stranded on a triangular You’re stranded on a triangular shaped island. The rescue ship canshaped island. The rescue ship canonly dock on one side of the island only dock on one side of the island but you don’t know which side. At but you don’t know which side. At which point of concurrency would which point of concurrency would you set up camp so you are anyou set up camp so you are anequalequal distance from all 3 sides?distance from all 3 sides?

INCENTERINCENTER

What if the ship could only dock What if the ship could only dock at the verticies? at the verticies? Would you change the location Would you change the location of the camp ?of the camp ?If so, where?If so, where?

YES,YES, CIRCUMCENTERCIRCUMCENTER

The End

Worksheet

BCBC

NMNM

77

1616

33

ACAC

88

8828.28. TrueTrue

29.29. FalseFalse

30.30. TrueTrue