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22 Cards in this Set
- Front
- Back
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perpendicular bisector
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…of a side of a triangle is a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side.
Property: Any point on a perpendicular bisector is equidistant from two vertices |
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concurrent lines
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three or more lines intersecting at a common point
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point of concurrency
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the point of intersection of concurrent lines
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circumcenter
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the point of concurrency of the perpendicular bisectors of a triangle
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Circumcenter Theorem
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The circumcenter of a triangle is equidistant from the vertices of the triangles.
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angle bisectors
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Property:
Any point on the angle bisector is equidistant from the sides of the triangle. |
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incenter
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the point of concurrency of the angle bisectors of a triangle
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Incenter Theorem
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The incenter of a triangle is equidistant from each side of the triangle.
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median
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segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite it
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centroid
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the point of concurrency of the medians of a triangle
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Centroid Theorem
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The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.
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altitude
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...of a triangle is a segment from a vertex through the line containing the opposite side and is perpendicular to that side
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orthocenter
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the point of concurrency of the altitudes of the triangle
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Exterior Angle Inequality Theorem
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If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its remote interior angles.
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If one side of a triangle is longer than another side, then…
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...the angle opposite the longer side has a greater measure than the angle opposite the shorter side
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If one angle of a triangle has a greater measure than another angle, then…
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...the side opposite the greater angle is longer than the side opposite the smaller angle.
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Triangle Inequality Theorem
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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shortest distance from a point
to a line is… |
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shortest distance from a point
to a plane is… |
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SAS Inequality Theorem
(Hinge Theorem) |
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SSS Inequality Theorem
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