Ninth Grade Mathematics Geometry Definitions, Theorems, Postulates, and Corollaries – Flashcards
Unlock all answers in this set
Unlock answersquestion
Ruler Postulate
answer
The points on a line can be paired with the real numbers in such a way that only two points can have coordinates zero and one. Once a coordinate system has been chosen in this way the distance between only two points equals the absolute value of the difference of their coordinates.
question
Segment Addition Postulate
answer
If B is between A and C, then AB+BC=AC.
question
Definition of Congruent Segments
answer
Segments with equal lengths.
question
Definition of a Midpoint
answer
The point that divides the segment into two congruent segments.
question
Definition of a Bisector
answer
A line, segment, or ray that intersects the segment at its midpoint.
question
Definition of an Angle
answer
An angle is the union of two rays with a common endpoint.
question
Angle Addition Postulate
answer
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.
question
Definition of Adjacent Angles
answer
Two angles in the same plane with a common vertex and a common side between them.
question
Postulate 6
answer
Two points determine a line.
question
Postulate 7
answer
Three non collinear points determine a plane.
question
Postulate 9
answer
If two planes intersect, then their intersection is a line.
question
Theorem 1-1
answer
If two lines intersect, then they intersect in exactly one point.
question
Theorem 1-2
answer
Perpendicular lines form congruent right angles.
question
Definition of Perpendicular Angles
answer
Two lines intersect and form congruent adjacent angles.
question
Addition Property of Equality
answer
If A=B and C=D, then A+C=B+D.
question
Subtraction Property of Equality
answer
If A=B and C=D, than A-C=B-D.
question
Multiplication Property of Equality
answer
If A=B, then CA=CB.
question
Division Property of Equality
answer
If A=B, and C≠0, then A/C=B/C.
question
Substitution Property
answer
If A=B, then either A or B may be substituted in any algebraic expression.
question
Reflexive Property
answer
A=A.
question
Symmetric Property
answer
If A=B then B=A.
question
Transitive Property
answer
If A=B and B=C, then A=C.
question
Midpoint Theorem
answer
If point M is the midpoint of line segment AB, then line segment AM=1/2AB and line segment MB=1/2AB.
question
Angle Bisector Theorem
answer
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.
question
Definition of Supplementary Angles
answer
Two angles whose sum is 180.
question
Definition of Complementary Angles
answer
Two angles whose sum is 90.
question
Supplement Theorem
answer
If the exterior sides of two adjacent angles are opposite rays then they are supplementary.
question
Complement Theorem
answer
If the exterior sides of two adjacent angles are perpendicular rays, then they are complementary.
question
Theorem 2-7
answer
Supplements of congruent angles are congruent.
question
Theorem 2-8
answer
Compliments of congruent angles are congruent.
question
Theorem 2-3
answer
Vertical angles are congruent.
question
Definition of a Transveral Line
answer
A line which intersects two or more lines in different points.
question
Definition of Parallel Lines
answer
Coplanar lines that do not intersect.
question
Alternate Interior Angles Theorem
answer
If lines are parallel than alternate interior angles are congruent.
question
Corresponding Angles Postulate
answer
If lines are parallel than corresponding angles are congruent.
question
Same Side Interior Angles Theorem
answer
If lines are parallel than same side interior angles are supplementary.
question
Scalene Triangle
answer
A triangle that has no congruent sides
question
Isosceles Triangle
answer
A triangle that has two congruent sides.
question
Equilateral Triangle
answer
A triangle that has three congruent sides.
question
Acute Triangle
answer
A triangle that has three acute angles.
question
Obtuse Triangle
answer
A triangle that has one obtuse angle.
question
Right Triangle
answer
A triangle that has one right angle.
question
Equiangular Triangle
answer
A triangle that has three congruent angles.
question
Theorem 3-11
answer
The sum of the measures of the angles of a triangle is 180.
question
Corollary 1
answer
If 2 angles of one triangle are congruent to two angles of another triangle, the third angles are congruent.
question
Corollary 2
answer
Each angle of an equiangular triangle has a measure of 60.
question
Corollary 3
answer
In a triangle, there is at most one right or obtuse angle.
question
Corollary 4
answer
The acute angles of a right triangle are complementary.
question
Theorem 3-12
answer
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
