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134 Cards in this Set
- Front
- Back
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Commutative Property of Addition
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a+b=b+a
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Commutative Property of Multiplication
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ab=ba
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Associative Property of Addition
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(a+b)+c= a+(b+c)
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Associative Property of Multiplication
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(ab)c=a(bc)
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Distributive Property
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a(b+c)= ab+ac
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Reflexive Property
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a=a
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Transitive Property
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If a=b and b=c then a=c
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Symmetric Property
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If a=b then b=a
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Addition Property
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If a=b, then a+c=b+c. Also, if a=b and c=d, then ac=bd.
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Division Property
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If a=b, then a/c=b/c, provided C is not 0. Also, If a=b and c=d, then a/c=b/d, if C is not 0 and D is not 0.
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Square root Property
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If a squared = b, then a=+- the square root of b.
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Zero Product
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if ab=0, then a=0 or b=0, or both a and b = zero.
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Line Postulate
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Exactly one line can be constructed through 2 points
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Line Intersection Postulate
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The intersection of 2 distict lines is at exactly one point
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Segment Duplication Postulate
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Exactly one segmant can be constructed congruent to another segment.
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Angle Duplication Postulate
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Exactly one angle can be constructed congruent to another angle
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Midpoint Postulate
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Exactly one midpoint can be constructed on any line
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Angle Bisector Postulate
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Exactly one angle bisector bacn we constructed on any angle.
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Parallel Postulate
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Through one point not on a given line, exactly one parallel line to the given line can be constructed.
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Perpendicular Postulate
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THrough a point not on a line, exactly one line perpendicular to the line can be constructed
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Segment Addition Postulate
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If point B is on line AC and between points A and C, then segment AB + segment BC = line AC.
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Angle Addition Postulate
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If point D lies in the interior of angle ABC, then the measure of angle ABD + the measure of angle DBC = the measure of angle ABC.
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Linear Pair Postulate
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If 2 angles are a linear pair, they are supplementary
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Cooresponding Angles Postulate
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If 2 parallel lines are cut by a transveral, then the cooresponding andlges are congruent.
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Converse to the Cooresponding Angles Postulate
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If 2 lines are cut by a transveral forming cooresponding angles, then the lines are parallel.
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SSS Congruence Postulate
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If the 3 sides of a triangle are congruent to the 3 sides of another triangle, then the 2 triangles are congruent.
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SAS Congruence Postulate
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If 2 sides and their included angle in one triangle are congruent to 2 sides and the included angle of another triangle, the triangles are congruent.
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ASA Congruence Postulate
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If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.
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Alternate Interior Angles Theorem
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If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
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Converse of the Alternate Interior Angles Theorem
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If alternate interior angles are congruent, then the twi lines cut by the transveral are parallel.
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Triangle Sum Theorem
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The sum of the measures of the anlges in a triangle is 180 degrees.
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Third Angle Theorem
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If two angles of one triangle are congruent to two angles of a second triangle, then the third pair of angles are congruent.
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Congruent and Supplementary Theorem
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If two angles are both congruent and supplementary, then each is a right angle.
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Supplements of Congruent Angles Theorem
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Supplements of congruent angles are congruent.
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Right Angles Are Congruent Theorem
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All right angles are congruent.
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Alternate Exterior Angles Theorem
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If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
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Converse of the Alternate Exterior Angles Theorem
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If two lines are cut by a transveral forming congruent alternate Exterior angles, then the lines are parallel.
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Interior Supplements Theorem
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If two lines are cut by a transveral, then the interior angles on the same side of the transveral are supplementary.
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Converse of the Interior Supplements Theorem
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If two linens are cut by a transversal forming interior angles on the same side of the transversal that are supplementary, then the lines are parallel.
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Parallel Transitivity Theorem
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If two lines in the same plane are parallel to the third line, they are parallel to each other.
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Perpendicular to Parallel Theorem
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If two lines in the same plane are perpendicular to a third line, then they are parallel to each other.
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SAA Congruence Theorem
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If 2 angles and a non included side of a triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent.
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Angle Bisector Theorem
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Any point on the bisector of an angleis equidistant from the sides of the angle.
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Perpendicular Bisector Theorem
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If a point is on the perpendicular bisector of a segment, then it is equally distant from the endpoints of the segment.
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Converse of the Perpendicular Bisector Theorem
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If a point is equidistant from the endpoints of a segment, then it is the perpendiculr bisector of the segment.
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Isosceles Triangle Theorem
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If a triangle is isosceles, then the base angles are congruent.
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Converse of the Isosceles Theorem
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If two angles of a triangle are congruent, then the triangle is isosceles
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Converse of the Angle Bisector Theorem
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If a point is equally distant from the sides of an angle, then it is on the bisector of the angle.
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Perpendicular Bisector Concurrency Theorem
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The three perpendiculare bisectors of the sides of a triangle are concurrent.
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Angle Bisector Concurrency Theorem
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The three angle bisectors of the sides of a triangle are concurrent.
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Triangle Exterior Angle Theorem
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remore interior angles.
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Quadrilateral Sum Theorem
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THe sum of the measures of the four angles of a quadrilateral is 360 degrees.
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Medians to the Congruent Sides Theorem
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In an isosceles triangle, the medians to the congruent sides are congruent.
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Angle Bisectors to the Congruent Sides Theorem
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In an isosceles triangle, the altitudes to the congruent sides are congruent.
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Altitudes to the Congruent Sides Theorem
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In an isosceles triangle, the altitudes to the congruent sides are congruent.
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Isosceles Triangle Vertex Angle Theorem
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The bisector of the vertex angle of an isosceles triangle is also the median and altitude to the base.
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Parallelogram Diangonal Lemma
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A diagonal of a parallelogram divides the parallelogram into two congruent triangles.
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Opposite Sides Theorem
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The opposite sides of a parallelogram are congruent
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Opposie Angles Theorem
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The opposite angles of a parallelogram are congruent
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Converse of the Opposite Sides Theorem
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If a figure is a parallelogram, then its opposite sides are congruent.
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Converse of the Opposite Angles Theorem
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If the opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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Oppiste Sides Parallel and Congruent Theorem
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If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
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Rhombus Angles Theorem
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Each diagonal of a rhombus bisects two opposite angles.
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Parallelogran Consecutive Angles Theorem
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The consecutive angles of a parallelogram are supplementary.
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Four Congruent Sides Rhombus Theorem
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If a quadrilateral has four congruent sides, then it is a rhombus.
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Four Congruent Angles Rectangle Theorem
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If a quadrilateral has four congruent angles, it is a rectangle
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Rectangle Diagonals Theorem
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The diangonals of a rectangle are congruent
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Converse of the Rectangle Diangonals Theorem
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If the diangonals of a prallelogram are congruent, then the parallelogram is a rectangle.
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Isosceles Trapezoid Theorem
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The base angles of an isosceles trapezoid are congruent.
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Isosceles Trapezoid Diagonals Theorem
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The diagonals of an isosceles trapezoid are congruent.
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Converse of the Rhombus Angles Theorem
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If a diagonal of a parallelogram bisects two opposite angles, then the parallelogram is a rhombus.
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Double Edged Straight Edge Theorem
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IF two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a rhombus.
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Tangent Theorem
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A tangent is perpendicular to the radius drwan to the point of tangency.
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Theorem
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No triangle has two right angles.
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Perpendicular Bisector of a Chord Theorem
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The perpendicular bisector of a chord passes through the center of the circle.
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Arc Addition Postulate
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If point B is one arc AC and between points A and C, then the measure of arc AB + the measure of arc BC = the measure of arc AC.
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Inscribed Angle Theorem
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The measure of an angle in a circle is half the measure of the central angle.
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Inscribed Angles Intersecting Arcs Theorem
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Inscribed angles that intercept the same or congruent arcs are congruent.
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Cylic Quadrilateral Theorem
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The opposite angles of an inscribed quadrilateral are supplementary.
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Parallel Secants Congruent Arc Theorem
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Parallel lines intercept cingruent arcs on a circle.
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Parallelogram Inscribed in a Circle Theorem
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If a parallelogram is inscribed within a circle, then the parallelogram is a rectangle.
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Tangent Segments Theorem
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Tangent segments from a point to a cirlce are congruent.
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Intersecting Chords Theorem
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The measure of an angle formed by two intersecting chords is half the sum of the measure of the two intercepted arcs.
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Reflexive Property of Similarity
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Any figure is similar to itself
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Symmetric Property of Similarity
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If Figure A is similar to Figure B, then Figure B is similar to Figure A
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Transitive Property of Similarity
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If Figure A is similar to Figure B and Figure B is similar to Figure C, then Figure A is similar to Figure C.
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AA Similarity Postulate
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If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
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SAS Similarity Theorem
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If two sides of a triangle are proportional to two sides of another triangle and the included angles are congruent then the two triangles are similar.
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SSS Similarity Theorem
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If the 3 sides of one triangle are proportional to the 3 sides of another triangle, then the 2 triangles are similar.
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Converse of the Opposite Angles Theorem
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If the opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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Oppiste Sides Parallel and Congruent Theorem
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If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
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Rhombus Angles Theorem
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Each diagonal of a rhombus bisects two opposite angles.
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Parallelogran Consecutive Angles Theorem
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The consecutive angles of a parallelogram are supplementary.
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Four Congruent Sides Rhombus Theorem
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If a quadrilateral has four congruent sides, then it is a rhombus.
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Four Congruent Angles Rectangle Theorem
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If a quadrilateral has four congruent angles, it is a rectangle
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Rectangle Diagonals Theorem
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The diangonals of a rectangle are congruent
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Converse of the Rectangle Diangonals Theorem
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If the diangonals of a prallelogram are congruent, then the parallelogram is a rectangle.
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Isosceles Trapezoid Theorem
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The base angles of an isosceles trapezoid are congruent.
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Isosceles Trapezoid Diagonals Theorem
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The diagonals of an isosceles trapezoid are congruent.
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Converse of the Rhombus Angles Theorem
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If a diagonal of a parallelogram bisects two opposite angles, then the parallelogram is a rhombus.
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Double Edged Straight Edge Theorem
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IF two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a rhombus.
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Tangent Theorem
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A tangent is perpendicular to the radius drwan to the point of tangency.
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Theorem
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No triangle has two right angles.
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Perpendicular Bisector of a Chord Theorem
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The perpendicular bisector of a chord passes through the center of the circle.
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Arc Addition Postulate
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If point B is one arc AC and between points A and C, then the measure of arc AB + the measure of arc BC = the measure of arc AC.
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Inscribed Angle Theorem
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The measure of an angle in a circle is half the measure of the central angle.
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Inscribed Angles Intersecting Arcs Theorem
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Inscribed angles that intercept the same or congruent arcs are congruent.
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Cylic Quadrilateral Theorem
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The opposite angles of an inscribed quadrilateral are supplementary.
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Parallel Secants Congruent Arc Theorem
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Parallel lines intercept cingruent arcs on a circle.
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Parallelogram Inscribed in a Circle Theorem
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If a parallelogram is inscribed within a circle, then the parallelogram is a rectangle.
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Tangent Segments Theorem
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Tangent segments from a point to a cirlce are congruent.
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Intersecting Chords Theorem
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The measure of an angle formed by two intersecting chords is half the sum of the measure of the two intercepted arcs.
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Reflexive Property of Similarity
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Any figure is similar to itself
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Symmetric Property of Similarity
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If Figure A is similar to Figure B, then Figure B is similar to Figure A
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Transitive Property of Similarity
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If Figure A is similar to Figure B and Figure B is similar to Figure C, then Figure A is similar to Figure C.
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AA Similarity Postulate
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If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
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SAS Similarity Theorem
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If two sides of a triangle are proportional to two sides of another triangle and the included angles are congruent then the two triangles are similar.
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SSS Similarity Theorem
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If the 3 sides of one triangle are proportional to the 3 sides of another triangle, then the 2 triangles are similar.
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Intersecting Secants Theorem
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If, then
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Corresponding Altitudes Theorem
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If two triangles are similar, then corresponding altitudes are proportional to the corresponding sides.
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Corresponding Medians Theorem
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If two triangels are similar, then corresponding medians are proportional to the corresponding sides.
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Corresponding Angle Bisector Theorem
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If two triangles are similar, then corresponding angle bisectors are proportional to the corresponding sides.
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Parallel Proportionality Theorem
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If a line passes through two sides of a triangle parallel to the third side, then it dived the two sides proportionally.
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Converse of the Parallel Proportionally Theorem
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If a line passes through two sides of a triangle dividing them proportionally, then it is parallel to the third side.
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Three Similar Right Triangles Theorem
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If you drop an altitude from the vertex of a right angle to its hypotenuse, then it divides the right triangle into two right triangles that are similar to each other and to the other right triangle.
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Altitude to Hypotenuse Theorem
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The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments on the hypotenuse.
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Pythagorean Theorem
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In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. If a and b are the lengths of the legs, and c is the length of the hypotenuse then a squared + b squared = c squared.
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Converse of the Pythagorean Theorem
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If the lengths of the three sides of a triangle satisfy the Pythagorean equation, then the triangle is a right triangle.
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Hypotenuse Leg Theorem
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If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse of one leg and another right triangle, then the two right triangles are congruent.
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Coordinate Midpoint Property
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IF x,y and x2,y2 are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are x1+x2/2,y1+y2/2
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Parallel Slope Property
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In a coordinate plane, two distinct lines are parallel if and only if their slopes are equal.
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Perpendicular Slope Property
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In a coordinate plane, two nonvertical lines are perpendicular if and only if their slopes are negatvie reciprocals of each other.
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Distance Formula
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The distance between points A(x1,y1) and B (x2,y2) is given by ABsquared= (x2-x1)=(y2-y1) or AB= the square root of (x2-x1) + (y2-y1)
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Square Diagonals Theorem
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The diagonals of a square are congruent and are perpendicular bisectors of each other.
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