Term
Acute Triangle
---CHAPTER-4--- |
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Definition
| Triangle with 3 acute sides. |
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Definition
| Triangle with 3 congruent acute angles. |
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Definition
| Triangle with 1 obtuse angle. |
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| Triangle with 1 right angle. |
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Definition
| triangle with 3 congruent sides. |
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Definition
| triangle with at least 2 congruent sides. |
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Definition
| triangle with no congruent sides. |
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Definition
| an extra line or segment drawn in a figure to help analyze geometric relationships. |
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Definition
| angles formed by one side of the triangle and the extension of an adjacent side. |
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Definition
| angles that are not adjacent to the exterior angle. |
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Definition
| a proof that uses statements written in boxes and arrows to show the logical progression of an argument. |
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Definition
| a theorem with a proof that follows as a direct result of another theorem. |
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Definition
| two geometric figures that have exactly the same shape and size. |
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Definition
| figures that are congruent to the corresponding parts of another polygon. |
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Definition
| matching parts of a figure. |
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Definition
| the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. |
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Definition
| the sum of the measures of the angles of a triangle is 180. |
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Definition
| if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. |
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Definition
| If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. |
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Definition
| an angle formed by two adjacent sides of a polygon. |
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Definition
| If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. |
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Definition
| the side located between two consecutive angles of a polygon. |
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Definition
| If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. |
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Definition
| if two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. |
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Term
| Legs of an isosceles triangle |
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Definition
| The two congruent sides of a triangle. |
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Definition
| The angle with the side of the triangle that are the legs. |
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Definition
| Two angles formed by the base and the congruent sides. |
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Term
| Isosceles triangle theorem |
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Definition
| if two sides of a triangle are congruent, then the angles opposite those sides are congruent. |
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Term
| Converse of isosceles triangle theorem |
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Definition
| If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
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Definition
| operation that maps an original geometric figure onto a new figure. |
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Definition
| A geometric figure before a transformation. |
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Definition
| The figure after a transformation. |
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Term
| Congruence transformation |
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Definition
| the image after may differ from the preimage, but the figures are still congruent. |
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Definition
| a transformation over a line called the line of reflection. |
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Definition
| a transformation that moves all points of the original figure the same distance in the same direction. |
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Definition
| a transformation around a fixed point called the center of rotation. |
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Definition
| proofs that use figures in the coordinate plane and algebra to prove geometric concepts. |
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Term
perpendicular bisector
----CHAPTER-5---- |
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Definition
| a bisector that is perpendicular to the segment. |
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Term
| perpendicular bisector theorem |
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Definition
| if a point is on the perpendicular bisector of a segment, then it is equidistant from the end points of the segment. |
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Term
| converse of the perpendicular bisector theorem |
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Definition
| if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |
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Definition
| when three or more lines interesect at a common point. |
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Definition
| the point where concurrent lines intersect. |
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Definition
| the point of concurrency of perpendicular bisectors. |
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Definition
| the perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle. |
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Definition
| if a point is on the bisector of an angle, then it is equidisttant from the sides of the angle. |
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Term
| converse of the angle bisector theorem |
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Definition
| if a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle. |
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Definition
| point of concurrency for angle bisectors. |
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Definition
| the angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of the triangle. |
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Definition
| a segment with endpoints being a vertex of a triangle and the midpoint of the other side. |
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Definition
| the point of concurrency for the medians of a triangle. |
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Definition
| the medians of a triangle intersect at a point called the centroid that is two thirds of the distance from each vertex to the midpoint of the opposite side. |
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Definition
| a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. |
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Definition
| the lines containing the altitudes of a triangle are concurrent, and they intersect at the orthocenter. |
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Definition
| assuming the conclusion is false to get the real answer. |
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Term
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Definition
| a proof where you assume what you are trying to prove is false, thus leading to a contradiction, proving your assumption false and proving what you were trying to prove as true. |
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Term
| triangle inequality theorem |
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Definition
| the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. |
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