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The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

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In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

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Includes: Centers of Concurrency, Ordering Angle/Side measurements by Side/Angle measurements, Example Problems, Etc.

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Includes: Centers of Concurrency, Ordering Angle/Side measurements by Side/Angle measurements, Example Problems, Etc.

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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. If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. If that is not true, then it is not possible to construct a triangle with the given side lengths.

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In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to the opposite side of the triangle. Meet at orthocenter

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A line or ray that divides an angle in half. For polygons, an angle bisector is a line that bisects an interior angle. Note: The angle bisectors of a triangle are concurrent and intersect at the incenter.

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In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

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A perpendicular bisector is a special kind of segment, ray, or line that. (1) intersects a given segment at a 90° angle, and. (2) passes through the given segment's midpoint. Segment CD is the perpendicular bisector to segment AB. Meet at circumcenter.