Questions and Answers
What is the meaning of the word 'Geometry'?
measurement of earth
How is a point represented?
by a fine dot marked with a sharp-edged pencil
Which of the following has a definite length?
A line extends endlessly in both directions.
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A _____ has one end point and extends endlessly in one direction.
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Define a parallelogram.
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What is the property of opposite sides in a parallelogram?
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Define a rhombus.
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What kind of objects are mentioned to have circular shapes in the content?
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What is the interior of a closed figure?
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What are linear boundaries of a figure?
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What are curvilinear boundaries of a figure?
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What is the interior of a closed figure?
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What is the exterior of a closed figure?
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Study Notes
Introduction to Geometry
- The word "Geometry" comes from two Greek words: "Geo" meaning earth and "metron" meaning measurement.
- Geometry was initially used in land measurement but is now widely used in various fields of daily life.
Points
- A point is a mark of position, represented by a capital letter (e.g., A, B, P, Q).
- A point has no length, breadth, or depth (or thickness).
Line Segments
- A line segment is a straight path between two points (e.g., AB).
- A line segment has a definite length, which can be measured using a ruler.
- A line segment can be represented by two different notations (e.g., AB or BA).
Lines
- A line is a set of points extending endlessly in both directions.
- A line has no end points.
- A line cannot be drawn on a paper, but a part of it can be represented by two arrow marks in opposite directions (e.g., AB ◄►).
Rays
- A ray is a line segment extended endlessly in one direction.
- A ray has one end point, called its initial point.
- A ray cannot be drawn on a paper, but a part of it can be represented by an arrow mark (e.g., AB).
Distinction between Line Segments, Lines, and Rays
- Line segment: has two end points, has a definite length, can be drawn on a paper.
- Line: has no end points, does not have a definite length, cannot be drawn on a paper.
- Ray: has one end point, does not have a definite length, cannot be drawn on a paper.
Surfaces
- A surface is a flat or curved boundary of a solid object.
- Examples of surfaces include the surface of a wall, table, blackboard, and sheet of paper.
Planes
- A plane is a flat surface that extends indefinitely in all directions.
- A plane cannot be drawn on a paper, but a part of it can be represented by a rectangle or parallelogram.
Intersecting Lines and Points of Intersection
- If two lines have a common point, they intersect at that point.
- The point of intersection is the point common to both lines.
Parallel Lines
- Two lines in a plane that do not intersect, even when produced, are called parallel lines.
- The distance between two parallel lines remains constant.
Concurrent Lines
- Three or more lines that pass through the same point are called concurrent lines.
- The point through which these lines pass is called the point of concurrency.
Curves
- A curve is a figure traced out using a sharp-edged pencil without lifting the pencil.
- Examples of curves include circles, ovals, and irregular curves.
Closed and Open Figures
- A closed figure begins and ends at the same point.
- An open figure does not end at the starting point.
Polygons
- A polygon is a simple closed figure formed by three or more line segments.
- Examples of polygons include triangles, quadrilaterals, pentagons, and hexagons.
Triangles and Quadrilaterals
- A triangle is a polygon with three sides.
- A quadrilateral is a polygon with four sides.
- Examples of quadrilaterals include rectangles, squares, parallelograms, and rhombi.
Circles
- A circle is a set of points equidistant from a fixed point called the center.
- A circle can be drawn by tracing the boundary of a coin or a circular object.
Interior and Exterior of a Closed Figure
- The interior of a closed figure is the part of the plane enclosed by the boundary.
- The exterior of a closed figure is the part of the plane lying outside the boundary.
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Description
Learn about the origin and meaning of the word Geometry, derived from Greek words 'Geo' and 'metron', and its ancient application in land measurement.
