Geometry Definitions, Postulates, and Theorems
Geometry Definitions, Postulates and Theorems
Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude
Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement that can be proven Two angles formed by intersecting lines and facing in the opposite direction A line that intersects two lines in the same plane at different points Pairs of angles formed by two lines and a transversal that make an F pattern Pairs of angles formed by two lines and a transversal that make a C pattern Pairs of angles formed by two lines and a transversal that make a Z pattern Triangles in which corresponding parts (sides and angles) are equal in measure Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal) A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure A ray, line or segment that divides a segment into two parts of equal measure The sides of equal measure in an isosceles triangle The third side of an isosceles triangle Having angles that are all equal in measure A line that bisects a segment and is perpendicular to it A segment from a vertex of a triangle perpendicular to the line containing the opposite side
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Definitions, Postulates and Theorems
Definitions Name Geometric mean Definition Visual Clue The value of x in proportion a/x = x/b where a, b, and x are positive numbers (x is the geometric mean between a and b) For an acute angle of a right triangle, the ratio of the side opposite the angle to the measure of the hypotenuse. (opp/hyp) For an acute angle of a right triangle the ratio of the side adjacent to the
Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude
Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement that can be proven Two angles formed by intersecting lines and facing in the opposite direction A line that intersects two lines in the same plane at different points Pairs of angles formed by two lines and a transversal that make an F pattern Pairs of angles formed by two lines and a transversal that make a C pattern Pairs of angles formed by two lines and a transversal that make a Z pattern Triangles in which corresponding parts (sides and angles) are equal in measure Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal) A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure A ray, line or segment that divides a segment into two parts of equal measure The sides of equal measure in an isosceles triangle The third side of an isosceles triangle Having angles that are all equal in measure A line that bisects a segment and is perpendicular to it A segment from a vertex of a triangle perpendicular to the line containing the opposite side
Page 1 of 11
Definitions, Postulates and Theorems
Definitions Name Geometric mean Definition Visual Clue The value of x in proportion a/x = x/b where a, b, and x are positive numbers (x is the geometric mean between a and b) For an acute angle of a right triangle, the ratio of the side opposite the angle to the measure of the hypotenuse. (opp/hyp) For an acute angle of a right triangle the ratio of the side adjacent to the