Concurrency HGEO

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Last updated 7:56 PM on 12/11/22
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30 Terms

1
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Midsegment
Joins two midpoints of two sides of a triangle
Parallel and half the length of the 3rd side a triangle
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Perpendicular Bisector
The bisector is also perpendicular
Equidistant (same distance) from the endpoints of the segments
3
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Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
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Converse of Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector
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Angle Bisector
A ray, segment, or line, that divides an angle into two congruent angles
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Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides
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Converse of Angle Bisector Theorem
If a point in the interior of a triangle is equidistant from the sides of the angle, then it is on the angle bisector
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Median
A segment that connects a vertex to midpoint of the opposite side
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Alititude
A perpendicular segment that goes from a vertex to the opposite side
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Circumcenter
Perpendicular Bisector
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Circumcenter Theorem
The circumcenter is equidistant to the vertices of the triangle
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Circumcenter location
Acute triangle - inside
Obtuse - outside
Right - On
Same as orthocenter locations
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Incenter
Angle Bisector
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Incenter theorem
The incenter is equidistant to the sides of the triangle
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Incenter/Centroid location
ALWAYS INSIDE
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Incenter
Always "in the center", always inside the triangle
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Centroid
Median
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Centroid Theorem
The centroid is the balancing point of the triangle.
2/3 and 1/3 split of the median (longer one goes from the centroid to the vertex)
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Centroid/Incenter location
ALWAYS INSIDE
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Orthocenter
Altitude
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Orthocenter location
Acute - Inside
Obtuse - Outside
Right - on
Same as circumcenter locations
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Triangle Inequality Theorem
The sum of the lengths of any two sides must be greater than the third side (shortcut: add the two shortest lengths and compare to the other side)
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Scalene Triangle Inequality
The longest side is opposite the largest angle
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The point that is equidistant from the sides of ∆ABC is called the _____.
Incenter
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The point that is equidistant from the vertices of ∆ABC is called the _____
Circumcenter
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Centroid facts
The point that divides the median into a 2/3, 1/3 split is called the triangle’s _____
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In what kind of triangle does the circumcenter lie on of the circle?
Right Triangle
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Circumcenter
=dist. to vertices
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Incenter
=dist. to sides
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Centroid formula
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)

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