Basics of Geometry :
In its simplest form, geometry is the mathematical study of shapes and space. Geometry can deal with flat, two-dimensional shapes, such as squares and circles, or three-dimensional shapes with depth, such as cubes and spheres.
Before diving into two-dimensional and three-dimensional shapes, consider the basic geometric objects that create these shapes: points, lines, line segments, rays, and planes.
Patterns and Inductive Reasoning :
Much of the reasoning in geometry consists of three stages.
(i) Look for a pattern. Look at several examples. Use diagram and tables to help discover a pattern.
(ii) Make a conjecture. Use the examples to make a general conjecture. A conjecture is an unproven statement that is based on observations. Discuss the conjecture with others. Modify the conjecture, if necessary.
(iii) Verify the conjecture. Use the logical reasoning to verify that the conjecture is true in all cases.
Looking for patterns and making conjectures is part of a process called inductive reasoning.
A point has no dimension and it is usually represented by a small dot.
A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions.
A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. We have to imagine that the plane extends without end, even though the drawing of a plane appears to have edges.
In geometry, segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points.
An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.
The midpoint of a segment is the point that divides or bisects, the segment into two congruent segments.
Segment Bisector :
A segment bisector is a segment, ray, line, or plane that intersects a segment at its mid point.
Angle bisector :
An angle bisector is a ray that divides an angle into two adjacent angles that are congruent.
Vertical Angles and Linear Pair :
Two angles are vertical angles, if their sides form two pairs of opposite rays.
Two adjacent angles are a linear pair, if their non-common sides are opposite rays.
Complementary Angles :
Two angles are complementary angles, if the sum of their measures is 90⁰.
Supplementary Angles :
Two angles are supplementary angles, if the sum of their measures is 180⁰.
Perimeter is a path that surrounds a two dimensional shape. The term may be used either for the path or its length it can be thought of as the length of the outline of a shape.
The perimeter of a circle or ellipse is called its circumference. In other words, the distance around the edge of a circle or any curvy shape.
Area of an object is defined as the space occupied by the object on a flat surface. The area of a shape can be measured by comparing the shape to squares of a fixed size.
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