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84 Cards in this Set
- Front
- Back
3 undefined terms in geometry
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point, line, plane
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space
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set of all points
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collinear
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a set of points is collinear if there is a line that contains all the points of that set.
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coplanar
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a set of points is coplanar if they are all contained in the same plane.
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Distance Postulate
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to every two different points, there corresponds a unique positive number.
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Ruler Postulate
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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.
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Betweeness of points
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For one point to be between two other points all 3 must be different points on the same line.
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Segment Addition Postulate
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If B is between A and C, then AB+BC=AC
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Line Postulate
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For every two different points there is exactly one line that contains both points.
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Segment
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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.
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Ray
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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
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Opposite Rays
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If A is between B and C, then AB and Ac are opposite rays. Opposite rays form a line.
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midpoint
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U is the midpoint of FN if U is between F and N and UF=UN
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Bisector of a segment
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Any line, segment, ray or plane that intersects a segment at its midpoint. (A bisector splits something into two equal or congruent parts.
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Angle
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The union of two non-collinear rays with a common endpoint.
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Angle Measurement Postulate
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To every angle there corresponds a measure between 0 and 180 degrees.
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Angle Addition Postulate
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If H is in the interior of angle TAM the m of angle HAT + m of angle HAM= m of angle TAM.
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Linear Pair
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If EL and EG are opposite rays and EY is any other ray, then angle YEL and angle GEy form a linear pair.
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Adjacent Angles
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Two angles are adjacent if they share a common vertex and a common side, but share no common interior points.
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Supplementary Angles
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If the sum of two angle's measures = 180 degrees then the two angles are supplementary.
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Linear Pair Postulate
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If two angles form a linear pair, then they are supplementary.
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Congruent Angles
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Two (or more) angles are congruent if they have the same measure
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Angle Bisector
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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
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Plane Postulate
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Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane
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Flat plane Postulate
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If two points are in a plane, then the line that contains the points is also in that plane.
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Intersection of Planes Postulate
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If two planes intersect, then their intersection is a line.
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Intersection of Lines Theorem
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If two lines intersect, then they intersect at exactly one point.
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Midpoint Theorem
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If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB
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Angle Bisector Theorem
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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
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Complementary Angles
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If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.
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Right Angle
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An angle whose measure is 90 degrees.
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Acute Angle
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An angle whose measure is less than 90 degrees.
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Obtuse Angle
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An angle whose measure is greater than 90 degrees and less than 180 degrees.
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Vertical Angles
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Two angles are vertical angles if their sides form two pairs of opposite rays.
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Vertical Angle Theorem
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Vertical angles are congruent.
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Complement Theorem
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Complements of Congruent Angles are congruent.
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Exterior sides adjacent angles theorem
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If the exterior sides of adjacent angles are perpendicular then the angles are complementary.
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Right Angle Theorem
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If two angles are right angles then they are congruent.
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Supplementary Right Angle Theorem
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If two angles are supplementary and congruent, then they are both right angles.
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Congruent Linear Pair Theorem
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If the angles in a linear pair are congruent then each is a right angle.
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Intersection of Planes Postulate
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If two planes intersect, then their intersection is a line.
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Intersection of Lines Theorem
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If two lines intersect, then they intersect at exactly one point.
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Midpoint Theorem
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If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB
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Angle Bisector Theorem
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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
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Complementary Angles
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If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.
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Right Angle
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An angle whose measure is 90 degrees.
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Acute Angle
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An angle whose measure is less than 90 degrees.
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Obtuse Angle
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An angle whose measure is greater than 90 degrees and less than 180 degrees.
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Vertical Angles
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Two angles are vertical angles if their sides form two pairs of opposite rays.
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Vertical Angle Theorem
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Vertical angles are congruent.
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Complement Theorem
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Complements of Congruent Angles are congruent.
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Exterior sides adjacent angles theorem
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If the exterior sides of adjacent angles are perpendicular then the angles are complementary.
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Right Angle Theorem
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If two angles are right angles then they are congruent.
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Supplementary Right Angle Theorem
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If two angles are supplementary and congruent, then they are both right angles.
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Congruent Linear Pair Theorem
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If the angles in a linear pair are congruent then each is a right angle.
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Intersection of Planes Postulate
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If two planes intersect, then their intersection is a line.
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Intersection of Lines Theorem
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If two lines intersect, then they intersect at exactly one point.
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Midpoint Theorem
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If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB
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Angle Bisector Theorem
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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
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Complementary Angles
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If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.
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Right Angle
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An angle whose measure is 90 degrees.
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Acute Angle
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An angle whose measure is less than 90 degrees.
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Obtuse Angle
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An angle whose measure is greater than 90 degrees and less than 180 degrees.
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Vertical Angles
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Two angles are vertical angles if their sides form two pairs of opposite rays.
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Vertical Angle Theorem
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Vertical angles are congruent.
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Complement Theorem
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Complements of Congruent Angles are congruent.
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Exterior sides adjacent angles theorem
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If the exterior sides of adjacent angles are perpendicular then the angles are complementary.
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Right Angle Theorem
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If two angles are right angles then they are congruent.
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Supplementary Right Angle Theorem
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If two angles are supplementary and congruent, then they are both right angles.
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Congruent Linear Pair Theorem
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If the angles in a linear pair are congruent then each is a right angle.
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Acute complementary theorem
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If two angles are complementary then both are acute angles.
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Congruent Triangles
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Two triangles are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent.
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SSS Postulate
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If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
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SAS Postulate
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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.
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ASA Postulate
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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.
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CPCTC
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C orresponding P arts of C ongruent T riangles are C ongruent.
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Triangle
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If A,B and C are 3 non-collinear points, then the union of segment AB, segment BC and segment AC forms a triangle.
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Scalene Triangle
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A triangle with no congruent sides.
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Isosceles Triangle
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A triangle with two congruent sides.
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Equilateral Triangle
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A triangle with all sides congruent.
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Isosceles Triangle Theorem (I.T.T.)
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If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
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Converse Isosceles Triangle Theorem (C.I.T.T.)
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If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
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Median
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the median of a triangle is a segment from a vertexto a midpoint of the opposite side.
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Altitude
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An altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side.
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