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84 Cards in this Set
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 Back
3 undefined terms in geometry

point, line, plane


space

set of all points


collinear

a set of points is collinear if there is a line that contains all the points of that set.


coplanar

a set of points is coplanar if they are all contained in the same plane.


Distance Postulate

to every two different points, there corresponds a unique positive number.


Ruler Postulate

the points on a line can be set up in correspondence with the real numbers in such a manner that the distance between any two pointsis equal to the absolute value of the difference between the coordinates of the two points.


Betweeness of points

For one point to be between two other points all 3 must be different points on the same line.


Segment Addition Postulate

If B is between A and C, then AB+BC=AC


Line Postulate

For every two different points there is exactly one line that contains both points.


Segment

For any two points X and O the segment joining X and O is the union of X and O and all points between X and O.


Ray

Let A and B be two points. The ray AB is the union of AB and all points C such that B is between A and C


Opposite Rays

If A is between B and C, then AB and Ac are opposite rays. Opposite rays form a line.


midpoint

U is the midpoint of FN if U is between F and N and UF=UN


Bisector of a segment

Any line, segment, ray or plane that intersects a segment at its midpoint. (A bisector splits something into two equal or congruent parts.


Angle

The union of two noncollinear rays with a common endpoint.


Angle Measurement Postulate

To every angle there corresponds a measure between 0 and 180 degrees.


Angle Addition Postulate

If H is in the interior of angle TAM the m of angle HAT + m of angle HAM= m of angle TAM.


Linear Pair

If EL and EG are opposite rays and EY is any other ray, then angle YEL and angle GEy form a linear pair.


Adjacent Angles

Two angles are adjacent if they share a common vertex and a common side, but share no common interior points.


Supplementary Angles

If the sum of two angle's measures = 180 degrees then the two angles are supplementary.


Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.


Congruent Angles

Two (or more) angles are congruent if they have the same measure


Angle Bisector

If D is in the interior of angle ABC and angle ABD is congruent to angle DBC, then ray BD is the bisector of angle ABC


Plane Postulate

Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane


Flat plane Postulate

If two points are in a plane, then the line that contains the points is also in that plane.


Intersection of Planes Postulate

If two planes intersect, then their intersection is a line.


Intersection of Lines Theorem

If two lines intersect, then they intersect at exactly one point.


Midpoint Theorem

If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB


Angle Bisector Theorem

If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC


Complementary Angles

If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.


Right Angle

An angle whose measure is 90 degrees.


Acute Angle

An angle whose measure is less than 90 degrees.


Obtuse Angle

An angle whose measure is greater than 90 degrees and less than 180 degrees.


Vertical Angles

Two angles are vertical angles if their sides form two pairs of opposite rays.


Vertical Angle Theorem

Vertical angles are congruent.


Complement Theorem

Complements of Congruent Angles are congruent.


Exterior sides adjacent angles theorem

If the exterior sides of adjacent angles are perpendicular then the angles are complementary.


Right Angle Theorem

If two angles are right angles then they are congruent.


Supplementary Right Angle Theorem

If two angles are supplementary and congruent, then they are both right angles.


Congruent Linear Pair Theorem

If the angles in a linear pair are congruent then each is a right angle.


Intersection of Planes Postulate

If two planes intersect, then their intersection is a line.


Intersection of Lines Theorem

If two lines intersect, then they intersect at exactly one point.


Midpoint Theorem

If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB


Angle Bisector Theorem

If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC


Complementary Angles

If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.


Right Angle

An angle whose measure is 90 degrees.


Acute Angle

An angle whose measure is less than 90 degrees.


Obtuse Angle

An angle whose measure is greater than 90 degrees and less than 180 degrees.


Vertical Angles

Two angles are vertical angles if their sides form two pairs of opposite rays.


Vertical Angle Theorem

Vertical angles are congruent.


Complement Theorem

Complements of Congruent Angles are congruent.


Exterior sides adjacent angles theorem

If the exterior sides of adjacent angles are perpendicular then the angles are complementary.


Right Angle Theorem

If two angles are right angles then they are congruent.


Supplementary Right Angle Theorem

If two angles are supplementary and congruent, then they are both right angles.


Congruent Linear Pair Theorem

If the angles in a linear pair are congruent then each is a right angle.


Intersection of Planes Postulate

If two planes intersect, then their intersection is a line.


Intersection of Lines Theorem

If two lines intersect, then they intersect at exactly one point.


Midpoint Theorem

If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB


Angle Bisector Theorem

If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC


Complementary Angles

If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.


Right Angle

An angle whose measure is 90 degrees.


Acute Angle

An angle whose measure is less than 90 degrees.


Obtuse Angle

An angle whose measure is greater than 90 degrees and less than 180 degrees.


Vertical Angles

Two angles are vertical angles if their sides form two pairs of opposite rays.


Vertical Angle Theorem

Vertical angles are congruent.


Complement Theorem

Complements of Congruent Angles are congruent.


Exterior sides adjacent angles theorem

If the exterior sides of adjacent angles are perpendicular then the angles are complementary.


Right Angle Theorem

If two angles are right angles then they are congruent.


Supplementary Right Angle Theorem

If two angles are supplementary and congruent, then they are both right angles.


Congruent Linear Pair Theorem

If the angles in a linear pair are congruent then each is a right angle.


Acute complementary theorem

If two angles are complementary then both are acute angles.


Congruent Triangles

Two triangles are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent.


SSS Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.


SAS Postulate

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.


ASA Postulate

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.


CPCTC

C orresponding P arts of C ongruent T riangles are C ongruent.


Triangle

If A,B and C are 3 noncollinear points, then the union of segment AB, segment BC and segment AC forms a triangle.


Scalene Triangle

A triangle with no congruent sides.


Isosceles Triangle

A triangle with two congruent sides.


Equilateral Triangle

A triangle with all sides congruent.


Isosceles Triangle Theorem (I.T.T.)

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.


Converse Isosceles Triangle Theorem (C.I.T.T.)

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.


Median

the median of a triangle is a segment from a vertexto a midpoint of the opposite side.


Altitude

An altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side.
