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Rel. in Triangles
Relatonships in Triangles - Midsegments, Concurrent Lines, etc.
Question | Answer |
---|---|
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. |