Introduction-to-Geometry (1)Building Blocks of Geometry .pptx

Building Blocks of Geometry

1. Introduction to Geometry Geometry is the fundamental branch of mathematics that deals with the study of shapes, sizes, and spatial relationships. It underpins our understanding of the physical world around us, from the smallest atoms to the grandest celestial bodies. This introduction to geometry will explore the building blocks and core concepts that form the foundation of this essential discipline. by Kayra Theress Gubat

2. Undefined Terms in Geometry 1 Point A point is the most fundamental undefined term in geometry. It has no size or dimension, representing a specific location in space. 2 Line A line is another undefined term, representing a one-dimensional path that extends infinitely in both directions. 3 Plane A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is the foundation for much of geometric reasoning.

3. Fundamental Shapes: Point, Line, Plane Point A point has no dimensions and represents a specific location in space. It is the most basic building block of geometry. Line A line is a one-dimensional object that extends infinitely in two directions. It is defined by two distinct points and has no width or thickness. Plane A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is the foundation for many geometric shapes and constructions.

4. Space, Figure, Coplanar, Collinear Points, Noncollinear and Noncoplanar 1 Space Space is the three-dimensional environment in which all geometric objects and shapes exist. It is the foundation for all geometric concepts and relationships. 2 Figure A figure is any geometric object, such as a point, line, plane, or any combination of these fundamental shapes. 3 Collinear Points Collinear points are points that lie on the same line. They share a common one-dimensional path.

5. Physical Model and Definition of Collinear Points, Coplanar Points, Intersecting Lines Collinear Points Collinear points are points that lie on the same line. They share a common one-dimensional path and can be represented by a single line segment. Coplanar Points Coplanar points are points that lie on the same plane. They share a common two-dimensional surface and can be represented by a single plane. Intersecting Lines Intersecting lines are two or more lines that cross at a single point. This point of intersection is a unique location in space where the lines meet.

6. Physical Model and Definition of Perpendicular Line, Parallel Line, Concurrent Line Perpendicular Lines Perpendicular lines are lines that intersect at right angles, forming four equal angles. They are often represented by the symbol ⊥. Parallel Lines Parallel lines are lines that never intersect and maintain a constant distance between them. They are often represented by the symbol ∥. Concurrent Lines Concurrent lines are lines that intersect at a single point. This point of intersection is called the point of concurrency.

7. Physical Model and Definition of Parallel Plane, Skew Line and Intersecting Plane Parallel Planes Parallel planes are two planes that maintain a constant distance between them and never intersect. They are often represented by the symbol ∥. Skew Lines Skew lines are two or more lines that are not parallel and do not intersect. They exist in three-dimensional space and maintain a constant distance between them. Intersecting Planes Intersecting planes are two or more planes that cross at a common line. This line of intersection is a unique location where the planes meet.

8. Angles and their Measurement 1 Acute Angle An acute angle is an angle that measures less than 90 degrees. It is a sharp, narrow angle that is less than a right angle. 2 Obtuse Angle An obtuse angle is an angle that measures more than 90 degrees. It is a wide, open angle that is greater than a right angle. 3 Right Angle A right angle is an angle that measures exactly 90 degrees. It is formed by the intersection of two perpendicular lines and is often represented by the symbol ⊥.

9. Polygons: Triangles, Quadrilaterals, and Beyond Triangles Triangles are the most fundamental polygons, consisting of three straight sides and three angles. They are the building blocks of many more complex geometric shapes. Quadrilaterals Quadrilaterals are polygons with four straight sides and four angles. They include shapes such as squares, rectangles, and parallelograms. Beyond Geometry extends beyond triangles and quadrilaterals, encompassing a wide range of polygons with five or more sides, as well as three-dimensional shapes like cubes, pyramids, and spheres.

10. Circles and their Properties Radius The distance from the center of the circle to the edge, measured in a straight line. Diameter The distance across the circle, passing through the center. It is twice the radius. Circumference The distance around the circle. It is equal to 2π times the radius.