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84 Cards in this Set

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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 non-collinear 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 non-collinear 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 non-collinear 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.