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Points Of Concurrency
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Gravity
Terms in this set (14)
POC Medians
Centroid (center of gravity/balance point)
POC Altitudes
Orthocenter (can be outside the triangle, will be outside an obtuse triangle, will be inside acute triangle, orthocenter of a right triangle is at the vertex containing the right angle)
POC Perpendicular Bisectors
Circumcenter (doesn't have to go through vertex but can, could intersect outside of the triangle, equidistant to the vertices of a triangle)
POC Angle Bisectors
Incenter (does not bisect sides, incenter will always be in the interior, equidistant to the sides of a triangle, distance is from a perpendicular line from incenter to side)
Median
A line segment joining a vertex to the midpoint of the opposing side (doesn't bisect angles unless triangles are equilateral or isosceles)
Altitude
A line segment through a vertex and perpendicular to a line containing the base (doesn't bisect sides or angles unless triangles are equilateral or isosceles)
Perpendicular Bisector
A line that divides a line segment into two equal parts, making a right angle with the line segment (doesn't go through vertex)
Angle Bisector
A line that splits and angle into two equal angles (equidistant to the sides of the triangle)
Median Theorem
The centroid is 2/3 the distance from each vertex to the midpoint (2:1 ratio)
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints (circumcenter is equidistant to the vertices of a triangle)
Angle Bisector Theorem
The incenter is equidistant to the sides of a triangle.
How To Draw A Median
1. Open compass more than 1/2 along a triangle's side length
2. Draw an arc on one side
3. Repeat on the other side
4. Draw a line through intersecting points connecting to the opposite vertex
How To Draw An Angle Bisector
1. Draw an arc from the vertex of an angle
2. Draw two smaller arcs from the point where the original arc intersects the bigger one
3. Draw a line through the vertex and intersecting point
How To Draw A Perpendicular Bisector
1. Set compass to greater than 1/2 of the triangle's side length
2. Draw arcs on both endpoints of the line
3. Draw an intersecting line connecting the points through the triangle's side length
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