## Glossary of Math Theorems

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- 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.

- 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= (x2-x1)=(y2-y1) or AB= the square root of (x2-x1) + (y2-y1)

- Square Diagonals Theorem
- The diagonals of a square are congruent and are perpendicular bisectors of each other.