Shared Flashcard Set

Details

Geometry
N/A
61
Mathematics
10th Grade
08/30/2012
Click here to study/print these flashcards.

Create your own flash cards! Sign up here.

Additional Mathematics Flashcards

 

 

Cards

Term
Ruler Postulate Part 1
 Definition
The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1.
Term
Ruler Postulate Part 2
 Definition
Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.
Term
Segment Addition Postulate
 Definition
If B is between A & C then AB+BC=AC.
Term
Protractor Postulate
 Definition
On <-AB-> in a given plane, choose any point O between A & B. Consider OA-> & OB-> and all the rays that can be drawn from O on one side of <-AB->. These rays can be paired with the real numbers from 0 to 180 in such a way that: a. OA-> is paired with 0, and OB-> is paired with 180 b. If OP-> is paired with x, OQ-> with y, then m
Term
Angle Addition Postulate Part 1
 Definition
If point B lies in the interior of
Term
Angle Addition Postulate Part 2
 Definition
If , then m
Term
Points Containment Postulate
 Definition
A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points points not all in one plane.
Term
Points-Line Postulate
 Definition
Through any two points there is exactly one line.
Term
Points-Plane Postulate
 Definition
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.
Term
Points-Line-Plane Postulate
 Definition
If two points are in a plane, then the line that contains the points is in that plane.
Term
Planes Intersection Postulate
 Definition
If two planes intersect, then their intersection is a line.
Term
Theorem 1-1
 Definition
If two lines intersect, then they intersect in exactly one point.
Term
Theorem 1-2
 Definition
Through a line and a point not in the line there is exactly one plane.
Term
Theorem 1-3
 Definition
If two lines intersect, then exactly one plane contains the lines.
Term
Addition Property of Equality
 Definition
If a = b and c = d, then a + c = b + d.
Term
Subtraction Property of Equality
 Definition
If a = b and c = d, then a - c = b - d.
Term
Multiplication Property of Equality
 Definition
If a = b, then ca = cb.
Term
Division Property of Equality
 Definition
If a = b and c does not = 0, then a/c = b/c.
Term
Substitution Property of Equality
 Definition
If a = b, then either a or b can be substituted for the other in any equation (or inequality).
Term
Reflexive Property of Equality
 Definition
a = a
Term
Symmetric Property of Equality
 Definition
If a = b, then b = a.
Term
Transitive Property of Equality
 Definition
If a = b and b = c, then a = c.
Term
Reflexive Property of Congruence
 Definition
Term
Symmetric Property of Congruence
 Definition
If
Term
Transitive Property of Congruence
 Definition
If
Term
Midpoint Theorem
 Definition
If M is the midpoint of -AB-, then AM = 1/2AB.
Term
Angle Bisector Theorem
 Definition
If BX-> is the bisector of
Term
Theorem 2-3
 Definition
Vertical angles are congruent.
Term
Theorem 2-4
 Definition
If two lines are perpendicular, then they form congruent Adjacent angles.
Term
Theorem 2-5
 Definition
If two lines form congruent adjacent angles, then the lines are perpendicular.
Term
Theorem 2-6
 Definition
If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Term
Theorem 2-7
 Definition
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.
Term
Theorem 2-8
 Definition
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.
Term
Skew Lines
 Definition
Are non-coplanar lines.
Term
Postulate 10
 Definition
If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Term
Theorem 3-2
 Definition
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
Term
Theorem 3-3
 Definition
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Term
Theorem 3-4
 Definition
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.
Term
Postulate 11
 Definition
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Term
Theorem 3-5
 Definition
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
Term
Theorem 3-6
 Definition
If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.
Term
Theorem 3-7
 Definition
In a plane two lines perpendicular to the same line are parallel.
Term
Theorem 3-8
 Definition
Through a point outside a line, there is exactly one line parallel to the given line.
Term
Theorem 3-9
 Definition
Through a point outside a line, there is exactly one line perpendicular to the given line.
Term
Theorem 3-10
 Definition
Two lines parallel to a third line are parallel to each other.
Term
Theorem 3-11
 Definition
The sum of the measures of the angles of a triangle is 180.
Term
Theorem 3-11 Corollary 1
 Definition
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
Term
Theorem 3-11 Corollary 2
 Definition
Each angle of an equiangular triangle measures 60.
Term
Theorem 3-11 Corollary 3
 Definition
In a triangle there can be at most one right angle or obtuse angle.
Term
Theorem 3-11 Corollary 4
 Definition
The acute angles of a right triangle are complementary.
Term
Theorem 3-12
 Definition
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
Term
Theorem 3-13
 Definition
the sum of the measures of the angles of a convex polygon with n sides is (n-2)180.
Term
Theorem 3-14
 Definition
The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.
Term
SSS Postulate
 Definition
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Term
SAS Postulate
 Definition
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Term
ASA Postulate
 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.
Term
The Isosceles Triangle Theorem
 Definition
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Term
The Isosceles Triangle Theorem Corollary 1
 Definition
An equilateral triangle is also equiangular.
Term
The Isosceles Triangle Theorem Corollary 2
 Definition
An equilateral triangle has three 60* angles.
Term
The Isosceles Triangle Theorem Corollary 3
 Definition
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.
Term
Theorem 4-2
 Definition
If two angle of a triangle are congruent, then the sides opposite those angles are congruent.
Supporting users have an ad free experience!