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Geometry is a branch of mathematics concerned with the relations of points, lines, surfaces, solids and shapes.
A point is an exact location in space. They are shown as dots on a plane in two dimensions or a dot in space in three dimensions. A point is labeled with capital letters.
A line is a geometric figure that consists of an infinite number of points lined up straight that extend in both directions, forever, indicated by the arrows at the end.
A line segment is a part of a line with two endpoints. A line segment starts and stops at the two endpoints.
A ray is part of a line with one endpoint and extends in one direction forever.
A plane is a flat two dimensional surface. A plane can be identified by three points in the plane or by a capital letter. There is exactly one plane through three points. The intersection of two planes is a line.
An angle consists of two rays with a common endpoint. The two rays is called the side of the angle and the common endpoint is the vertex of the angle. Each angle has a measurement generated by the rotation about the vertex. The measure is determined by the rotation of the terminal side about the initial side. Angles can be classified based upon the measure.
Rules in Algebra and Geometry:
Postulates of Equality and Operations
Addition Property of Equality: if a = b, then a + c = b + c
Multiplication Property of Equality: if a = b, then a * c = b * c
Substitution Property of Equality: if a = b, then a can be substituted for b in any equation or inequality
Subtraction Property of Equality: if a = b, then a - c = b - c
Postulates of Inequality and Operations
Addition Property of Inequality: if a < > b, then a + c < > b + c
Multiplication Property of Inequality: if a < b and c > 0, then a * c < b * c
if a < b and c < 0, then a * c > b * c
Equation to Inequality Property: if a and b are positive, and a + b = c, then c > a and c > b
if a and b are negative, and a + b = c, then c < a and c < b
Subtraction Property of Inequality: if a < > b, then a - c < > b - c
Transitive Property of Inequality: if a < b and b < c, then a < c
Postulates of Operation
Commutative Property of Addition: a + b = b + a
Commutative Property of Multiplication: a * b = b * a
Distributive Property: a * (b + c) = a * b + a * c and vice versa
Perimeter and Area Geometry
Shape Games Geometry