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134 Cards in this Set
 Front
 Back
Commutative Property of Addition

a+b=b+a


Commutative Property of Multiplication

ab=ba


Associative Property of Addition

(a+b)+c= a+(b+c)


Associative Property of Multiplication

(ab)c=a(bc)


Distributive Property

a(b+c)= ab+ac


Reflexive Property

a=a


Transitive Property

If a=b and b=c then a=c


Symmetric Property

If a=b then b=a


Addition Property

If a=b, then a+c=b+c. Also, if a=b and c=d, then ac=bd.


Division Property

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.


Square root Property

If a squared = b, then a=+ the square root of b.


Zero Product

if ab=0, then a=0 or b=0, or both a and b = zero.


Line Postulate

Exactly one line can be constructed through 2 points


Line Intersection Postulate

The intersection of 2 distict lines is at exactly one point


Segment Duplication Postulate

Exactly one segmant can be constructed congruent to another segment.


Angle Duplication Postulate

Exactly one angle can be constructed congruent to another angle


Midpoint Postulate

Exactly one midpoint can be constructed on any line


Angle Bisector Postulate

Exactly one angle bisector bacn we constructed on any angle.


Parallel Postulate

Through one point not on a given line, exactly one parallel line to the given line can be constructed.


Perpendicular Postulate

THrough a point not on a line, exactly one line perpendicular to the line can be constructed


Segment Addition Postulate

If point B is on line AC and between points A and C, then segment AB + segment BC = line AC.


Angle Addition Postulate

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.


Linear Pair Postulate

If 2 angles are a linear pair, they are supplementary


Cooresponding Angles Postulate

If 2 parallel lines are cut by a transveral, then the cooresponding andlges are congruent.


Converse to the Cooresponding Angles Postulate

If 2 lines are cut by a transveral forming cooresponding angles, then the lines are parallel.


SSS Congruence Postulate

If the 3 sides of a triangle are congruent to the 3 sides of another triangle, then the 2 triangles are congruent.


SAS Congruence Postulate

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.


ASA Congruence Postulate

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.


Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.


Converse of the Alternate Interior Angles Theorem

If alternate interior angles are congruent, then the twi lines cut by the transveral are parallel.


Triangle Sum Theorem

The sum of the measures of the anlges in a triangle is 180 degrees.


Third Angle Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third pair of angles are congruent.


Congruent and Supplementary Theorem

If two angles are both congruent and supplementary, then each is a right angle.


Supplements of Congruent Angles Theorem

Supplements of congruent angles are congruent.


Right Angles Are Congruent Theorem

All right angles are congruent.


Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.


Converse of the Alternate Exterior Angles Theorem

If two lines are cut by a transveral forming congruent alternate Exterior angles, then the lines are parallel.


Interior Supplements Theorem

If two lines are cut by a transveral, then the interior angles on the same side of the transveral are supplementary.


Converse of the Interior Supplements Theorem

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.


Parallel Transitivity Theorem

If two lines in the same plane are parallel to the third line, they are parallel to each other.


Perpendicular to Parallel Theorem

If two lines in the same plane are perpendicular to a third line, then they are parallel to each other.


SAA Congruence Theorem

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.


Angle Bisector Theorem

Any point on the bisector of an angleis equidistant from the sides of the angle.


Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equally distant from the endpoints of the segment.


Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a segment, then it is the perpendiculr bisector of the segment.


Isosceles Triangle Theorem

If a triangle is isosceles, then the base angles are congruent.


Converse of the Isosceles Theorem

If two angles of a triangle are congruent, then the triangle is isosceles


Converse of the Angle Bisector Theorem

If a point is equally distant from the sides of an angle, then it is on the bisector of the angle.


Perpendicular Bisector Concurrency Theorem

The three perpendiculare bisectors of the sides of a triangle are concurrent.


Angle Bisector Concurrency Theorem

The three angle bisectors of the sides of a triangle are concurrent.


Triangle Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remore interior angles.


Quadrilateral Sum Theorem

THe sum of the measures of the four angles of a quadrilateral is 360 degrees.


Medians to the Congruent Sides Theorem

In an isosceles triangle, the medians to the congruent sides are congruent.


Angle Bisectors to the Congruent Sides Theorem

In an isosceles triangle, the altitudes to the congruent sides are congruent.


Altitudes to the Congruent Sides Theorem

In an isosceles triangle, the altitudes to the congruent sides are congruent.


Isosceles Triangle Vertex Angle Theorem

The bisector of the vertex angle of an isosceles triangle is also the median and altitude to the base.


Parallelogram Diangonal Lemma

A diagonal of a parallelogram divides the parallelogram into two congruent triangles.


Opposite Sides Theorem

The opposite sides of a parallelogram are congruent


Opposie Angles Theorem

The opposite angles of a parallelogram are congruent


Converse of the Opposite Sides Theorem

If a figure is a parallelogram, then its opposite sides are congruent.


Converse of the Opposite Angles Theorem

If the opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.


Oppiste Sides Parallel and Congruent Theorem

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.


Rhombus Angles Theorem

Each diagonal of a rhombus bisects two opposite angles.


Parallelogran Consecutive Angles Theorem

The consecutive angles of a parallelogram are supplementary.


Four Congruent Sides Rhombus Theorem

If a quadrilateral has four congruent sides, then it is a rhombus.


Four Congruent Angles Rectangle Theorem

If a quadrilateral has four congruent angles, it is a rectangle


Rectangle Diagonals Theorem

The diangonals of a rectangle are congruent


Converse of the Rectangle Diangonals Theorem

If the diangonals of a prallelogram are congruent, then the parallelogram is a rectangle.


Isosceles Trapezoid Theorem

The base angles of an isosceles trapezoid are congruent.


Isosceles Trapezoid Diagonals Theorem

The diagonals of an isosceles trapezoid are congruent.


Converse of the Rhombus Angles Theorem

If a diagonal of a parallelogram bisects two opposite angles, then the parallelogram is a rhombus.


Double Edged Straight Edge Theorem

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.


Tangent Theorem

A tangent is perpendicular to the radius drwan to the point of tangency.


Theorem

No triangle has two right angles.


Perpendicular Bisector of a Chord Theorem

The perpendicular bisector of a chord passes through the center of the circle.


Arc Addition Postulate

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.


Inscribed Angle Theorem

The measure of an angle in a circle is half the measure of the central angle.


Inscribed Angles Intersecting Arcs Theorem

Inscribed angles that intercept the same or congruent arcs are congruent.


Cylic Quadrilateral Theorem

The opposite angles of an inscribed quadrilateral are supplementary.


Parallel Secants Congruent Arc Theorem

Parallel lines intercept cingruent arcs on a circle.


Parallelogram Inscribed in a Circle Theorem

If a parallelogram is inscribed within a circle, then the parallelogram is a rectangle.


Tangent Segments Theorem

Tangent segments from a point to a cirlce are congruent.


Intersecting Chords Theorem

The measure of an angle formed by two intersecting chords is half the sum of the measure of the two intercepted arcs.


Reflexive Property of Similarity

Any figure is similar to itself


Symmetric Property of Similarity

If Figure A is similar to Figure B, then Figure B is similar to Figure A


Transitive Property of Similarity

If Figure A is similar to Figure B and Figure B is similar to Figure C, then Figure A is similar to Figure C.


AA Similarity Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.


SAS Similarity Theorem

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.


SSS Similarity Theorem

If the 3 sides of one triangle are proportional to the 3 sides of another triangle, then the 2 triangles are similar.


Converse of the Opposite Angles Theorem

If the opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.


Oppiste Sides Parallel and Congruent Theorem

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.


Rhombus Angles Theorem

Each diagonal of a rhombus bisects two opposite angles.


Parallelogran Consecutive Angles Theorem

The consecutive angles of a parallelogram are supplementary.


Four Congruent Sides Rhombus Theorem

If a quadrilateral has four congruent sides, then it is a rhombus.


Four Congruent Angles Rectangle Theorem

If a quadrilateral has four congruent angles, it is a rectangle


Rectangle Diagonals Theorem

The diangonals of a rectangle are congruent


Converse of the Rectangle Diangonals Theorem

If the diangonals of a prallelogram are congruent, then the parallelogram is a rectangle.


Isosceles Trapezoid Theorem

The base angles of an isosceles trapezoid are congruent.


Isosceles Trapezoid Diagonals Theorem

The diagonals of an isosceles trapezoid are congruent.


Converse of the Rhombus Angles Theorem

If a diagonal of a parallelogram bisects two opposite angles, then the parallelogram is a rhombus.


Double Edged Straight Edge Theorem

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.


Tangent Theorem

A tangent is perpendicular to the radius drwan to the point of tangency.


Theorem

No triangle has two right angles.


Perpendicular Bisector of a Chord Theorem

The perpendicular bisector of a chord passes through the center of the circle.


Arc Addition Postulate

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.


Inscribed Angle Theorem

The measure of an angle in a circle is half the measure of the central angle.


Inscribed Angles Intersecting Arcs Theorem

Inscribed angles that intercept the same or congruent arcs are congruent.


Cylic Quadrilateral Theorem

The opposite angles of an inscribed quadrilateral are supplementary.


Parallel Secants Congruent Arc Theorem

Parallel lines intercept cingruent arcs on a circle.


Parallelogram Inscribed in a Circle Theorem

If a parallelogram is inscribed within a circle, then the parallelogram is a rectangle.


Tangent Segments Theorem

Tangent segments from a point to a cirlce are congruent.


Intersecting Chords Theorem

The measure of an angle formed by two intersecting chords is half the sum of the measure of the two intercepted arcs.


Reflexive Property of Similarity

Any figure is similar to itself


Symmetric Property of Similarity

If Figure A is similar to Figure B, then Figure B is similar to Figure A


Transitive Property of Similarity

If Figure A is similar to Figure B and Figure B is similar to Figure C, then Figure A is similar to Figure C.


AA Similarity Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.


SAS Similarity Theorem

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.


SSS Similarity Theorem

If the 3 sides of one triangle are proportional to the 3 sides of another triangle, then the 2 triangles are similar.


Intersecting Secants Theorem

If, then


Corresponding Altitudes Theorem

If two triangles are similar, then corresponding altitudes are proportional to the corresponding sides.


Corresponding Medians Theorem

If two triangels are similar, then corresponding medians are proportional to the corresponding sides.


Corresponding Angle Bisector Theorem

If two triangles are similar, then corresponding angle bisectors are proportional to the corresponding sides.


Parallel Proportionality Theorem

If a line passes through two sides of a triangle parallel to the third side, then it dived the two sides proportionally.


Converse of the Parallel Proportionally Theorem

If a line passes through two sides of a triangle dividing them proportionally, then it is parallel to the third side.


Three Similar Right Triangles Theorem

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.


Altitude to Hypotenuse Theorem

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.


Pythagorean Theorem

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.


Converse of the Pythagorean Theorem

If the lengths of the three sides of a triangle satisfy the Pythagorean equation, then the triangle is a right triangle.


Hypotenuse Leg Theorem

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.


Coordinate Midpoint Property

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


Parallel Slope Property

In a coordinate plane, two distinct lines are parallel if and only if their slopes are equal.


Perpendicular Slope Property

In a coordinate plane, two nonvertical lines are perpendicular if and only if their slopes are negatvie reciprocals of each other.


Distance Formula

The distance between points A(x1,y1) and B (x2,y2) is given by ABsquared= (x2x1)=(y2y1) or AB= the square root of (x2x1) + (y2y1)


Square Diagonals Theorem

The diagonals of a square are congruent and are perpendicular bisectors of each other.
