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![Page 1: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/1.jpg)
Aim: The four centers of a Aim: The four centers of a triangletriangleDo Now: Match the description
with the correct center of a triangle.
The perpendicular
bisectors of the three sides meet
at the
The three altitudes meet at
the
Centroid
Incenter
Orthocenter
Circumcenter
The three medians meet at
theThe angle bisectors meet at
the
![Page 2: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/2.jpg)
CircumcenterCircumcenterPerpendicular bisectorsHow do you draw a perpendicular
bisector?
![Page 3: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/3.jpg)
CircumcenterCircumcenterWhat is a circumcenter?Hint: What is it the center of?
CLICK HERE
![Page 4: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/4.jpg)
CircumcenterCircumcenterWhere is the circumcenter
located ona) An acute triangleb) An obtuse trianglec) A right triangle
Inside the triangle
Outside the triangle
On the triangle
![Page 5: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/5.jpg)
CentroidCentroidMediansHow do you draw a median?
CLICK HERE
![Page 6: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/6.jpg)
CentroidCentroidWhat is special about the
medians that make a centroid?Hint: There is a ratio involved
![Page 7: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/7.jpg)
CentriodCentriodWhen is the centriod outside the
triangle?
A. When the triangle is acuteB. When the triangle is obtuseC. When the triangle is rightD. Never
![Page 8: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/8.jpg)
IncenterIncenterFormed by:Angle Bisectors
What is special about the incentor?
It is the center of a triangle that tangents all the sides
![Page 9: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/9.jpg)
IncenterIncenterFormed by angle bisectorsBisect this angle
![Page 10: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/10.jpg)
Properties of the IncenterProperties of the IncenterThe incenter is the center of the
triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides.
Always inside the triangle
CLICK HERE
![Page 11: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/11.jpg)
OrthocenterOrthocenterWhat forms an orthocenter?Altitudes
Shortcut:Instead of drawing all three altitudes two will also show the accurate orthocenter
![Page 12: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/12.jpg)
OrthocenterOrthocenterThe orthocenter is not always
inside the triangle. If the triangle is obtuse, it will be outside.
If the triangle is right it will be on the vertex of the right angle
CLICK HERE
![Page 13: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/13.jpg)
Regents Problem Regents Problem 1. The point where the medians of a
triangle are concurrent is called the [1] centroid [2] orthocenter
[3] incenter [4] circumcenter
2. The centroid of a triangle divides the medians into ratios of [1] 2:1 [2] 3:1 [3] 4:1 [4] 5:1
![Page 14: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/14.jpg)
Regents ProblemsRegents Problems3. The circumcenter of an acute triangle is
located inside the triangle. The circumcenter of an obtuse triangle is located outside the triangle. Where is the circumcenter of a right triangle located in relation to the triangle?
[1] on the triangle [2] outside the triangle [3] inside the triangle [4] the location varies
4. The orthocenter of a triangle is always
located inside the triangle. [1] TRUE [2] FALSE
![Page 15: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/15.jpg)
Regents ProblemsRegents Problems
5. It is possible to inscribe a circle in any shaped quadrilateral.
[1] TRUE [2] FALSE 6. The point of concurrence of the
angle bisectors of a triangle is always located inside the triangle.
[1] TRUE [2] FALSE
![Page 16: Aim: The four centers of a triangle Do Now: Match the description with the correct center of a triangle. The perpendicular bisectors of the three sides.](https://reader036.fdocuments.us/reader036/viewer/2022062715/56649d9e5503460f94a89177/html5/thumbnails/16.jpg)
Regents ProblemsRegents Problems7. The point of concurrence of the
perpendicular bisectors of a triangle is always located inside the triangle.
[1] TRUE [2] FALSE
8. The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.
[1] 16 [2] 18 [3] 24 [4] 36