special segments in triangles surrrre they are…. there are 4 special segments in a triangle....
TRANSCRIPT
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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CLICK HERECLICK HERE
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
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
• 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