Download Matching Orthocenter Circumcenter Incenter Centroid Where what

Matching
Where what crosses
What one of those Terms Tell you
3 Medians
2 Right Angles
3 Perpendicular Bisectors
Half Side = Half Side = ½ Whole
3 Altitudes
Half Angle = Half Angle = ½ Whole
1. Orthocenter
2. Circumcenter
3. Incenter
4. Centroid
Half Side = Half Side & 2 Right
Angles
3 Angle Bisectors
Centroid
Follows a Pattern where the Medians Cross.
The Big Piece is 2/3 of the whole Median.
The Small Piece is 1/3 of the whole Median.
The Small Piece is 1/2 of the Big Piece.
The Big Piece is *2 (Double) the Small Piece.
On the Picture the Big Pieces goes from the Centroid to the Vertex of Triangle. (or just Look)
On the Picture the Small Piece goes from the Centroid to the Midpoint of Side. (or just look)
On the Picture the whole Median goes from the Vertex to the Midpoint of the Opposite Side.
Do the Following Centroid Problems.
Big Piece = 20.
Small piece =*1/2 = 10
Whole = 30
Whole Line = 75
Small piece =1/3*75 = 25
Big Piece = 2/3*75=50
Small Piece = 14
Big Piece = *2 = 28
Whole = 42
Do the following Centroid Problems with Variables!
Big Piece = 2X+10
Small piece = X+5 (Half)
Whole = 3X+15 (Add them)
Whole Line = 30X+15
Small piece = 10X+5 (Third)
Big Piece = 20X+10 (Double Small)
Small Piece = X
Big Piece = 2X (Double small)
Whole = 3X (Add them)
Circumcenter. Follows a pattern where the Perpendicular Bisectors cross.
The triangle would fit perfectly inside a circle. (circle outside)
This the distance from the circumcenter to the TriangleVertex would be a Radius of the circle.
Since all Radii_ in a circle are equal.
The Line Segment from the Circumcenter to a vertex would be the same for all 3 vertex
IF R is Circumcenter of Triangle ABC
If RA = 10 then RB =10 & RC = 10
If RA = 4X then RB = 4X & RC = 4X
If RA = 3X+7 then RB =3X+7 & RC = 3X+7
So if RA = 3X+2 and RB = 14 you could set up a problem like 3X+2=14
So if RA = 4X+5 and RB = 2X+10 you could set up a problem like 4X+5=2X+10_
Incenter
Follows a pattern where the Altitude cross.
The triangle would fit a circle perfectly Inside the triangle.
The distance from the Incenter to the sides of the triangle would be a Raidus of the circle.
Since all Radii in a circle are equal.
The Line Segment from the Incenter to a Side would be the same for all 3 Sides
IF R is Incenter of Triangle ABC & AD BE CF were the Segments to the Sides
If RD = 4 then RE =4 & RF = 4
If RD = 2X then RE = 2X & RF = 2X
If RD = 3X+7 then RE = 3X+7 & RF = 3X+7
So if RD = 2X+6 and RE= 26 you could set up a problem like 2X+6=26
So if RD = 5X+25 and RB = 10X+15 you could set up a problem like 5X+25=10X+15