Ninth Grade Mathematics Geometry Definitions, Theorems, Postulates, and Corollaries – Flashcards
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Definition of a Bisector
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A line, segment, or ray that intersects the segment at its midpoint.
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Definition of an Angle
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An angle is the union of two rays with a common endpoint.
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Angle Addition Postulate
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If point B lies in the interior of angle AOC, then the measure of angle AOB+the angle of measure BOC=the measure of angle AOC.
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Definition of Adjacent Angles
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Two angles in the same plane with a common vertex and a common side between them.
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Postulate 6
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Two points determine a line.
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Postulate 7
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Three non collinear points determine a plane.
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Postulate 9
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If two planes intersect, then their intersection is a line.
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Theorem 1-1
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If two lines intersect, then they intersect in exactly one point.
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Theorem 1-2
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Perpendicular lines form congruent right angles.
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Definition of Perpendicular Angles
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Two lines intersect and form congruent adjacent angles.
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Addition Property of Equality
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If A=B and C=D, then A+C=B+D.
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Subtraction Property of Equality
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If A=B and C=D, than A-C=B-D.
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Multiplication Property of Equality
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If A=B, then CA=CB.
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Division Property of Equality
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If A=B, and C≠0, then A/C=B/C.
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Substitution Property
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If A=B, then either A or B may be substituted in any algebraic expression.
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Reflexive Property
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A=A.
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Symmetric Property
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If A=B then B=A.
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Transitive Property
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If A=B and B=C, then A=C.
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Midpoint Theorem
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If point M is the midpoint of line segment AB, then line segment AM=1/2AB and line segment MB=1/2AB.
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Angle Bisector Theorem
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If BX is the bisector of angle ABC, then the measure of angle ABX is 1/2 the measure of angle ABC and the measure of angle XBC is 1/2 the measure of angle ABC.
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Definition of Supplementary Angles
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Two angles whose sum is 180.
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Definition of Complementary Angles
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Two angles whose sum is 90.
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Supplement Theorem
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If the exterior sides of two adjacent angles are opposite rays then they are supplementary.
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Complement Theorem
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If the exterior sides of two adjacent angles are perpendicular rays, then they are complementary.
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Theorem 2-7
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Supplements of congruent angles are congruent.
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Theorem 2-8
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Compliments of congruent angles are congruent.
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Theorem 2-3
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Vertical angles are congruent.
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Definition of a Transveral Line
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A line which intersects two or more lines in different points.
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Definition of Parallel Lines
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Coplanar lines that do not intersect.
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Alternate Interior Angles Theorem
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If lines are parallel than alternate interior angles are congruent.
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Corresponding Angles Postulate
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If lines are parallel than corresponding angles are congruent.
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Same Side Interior Angles Theorem
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If lines are parallel than same side interior angles are supplementary.
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Scalene Triangle
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A triangle that has no congruent sides
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Isosceles Triangle
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A triangle that has two congruent sides.
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Equilateral Triangle
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A triangle that has three congruent sides.
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Acute Triangle
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A triangle that has three acute angles.
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Obtuse Triangle
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A triangle that has one obtuse angle.
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Right Triangle
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A triangle that has one right angle.
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Equiangular Triangle
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A triangle that has three congruent angles.
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Theorem 3-11
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The sum of the measures of the angles of a triangle is 180.
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Corollary 1
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If 2 angles of one triangle are congruent to two angles of another triangle, the third angles are congruent.
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Corollary 2
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Each angle of an equiangular triangle has a measure of 60.
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Corollary 3
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In a triangle, there is at most one right or obtuse angle.
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Corollary 4
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The acute angles of a right triangle are complementary.
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Theorem 3-12
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The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
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