# Concurrency HGEO

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Midsegment

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30 Terms
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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

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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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