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Rel. in Triangles

Relatonships in Triangles - Midsegments, Concurrent Lines, etc.

QuestionAnswer
If a point lies on the perpendicular bisector of a segment, then... it is equidistant from endpoints of the segment.
If a point is equidistant from the endpoints of a segment, then... it lies on the perpendicular bisector of the segment.
If a point lies on the bisector of an angle, then... it is equidistant from the sides of the angle.
If a point is equidistant from the sides of an angle, then... it lies on the bisector of the angle.
The segment joining the midpoints of two sides of a triangle is called the... midsegment.
If a segment joins the midpoints of two sides of a triangle, then... it is parallel to the third side and half its length.
The perpendicular bisectors of a triangle are concurrent at a point... equidistant from the vertices (circumcenter)
The angle bisectors of a triangle are concurrent at a point... equidistant from the sides (incenter).
The medians of a triangle are concurrent at a point... that is two thirds the distance from each vertex to the midpoint on the opposite side (centroid).
The altitudes of a triangle are concurrent at the... orthocenter.
The perpendicular bisectors of a triangle are... the lines that are perpendicular to the sides at their midpoints.
The angle bisectors of a triangle are... the lines that bisect each vertex.
The medians of a triangle are... the segments which connect each vertex with the midpoint of the opposite side.
The altitudes of a triangle are... the lines that travel through each vertex and are perpendicular to the opposite side.
If two sides of a triangle are not congruent, then... the longer side lies opposite the larger angle.
If two angles in a triangle are not congruent, then... the larger angle lies opposite the longer side.
The measure of an exterior angle of a triangle is equal to... the sum of the measures of the two remote interior angles.
Created by: mburke79