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Geometry - Types of Lines

Grade 3ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Point: A point is a tiny dot that represents a specific position in space. It has no length, breadth, or thickness. In geometry, we name a point using a capital letter, such as Point AA.

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Line Segment: A line segment is a straight path that connects two fixed points. It has a definite length that can be measured and has two endpoints. Visually, it is represented as a straight line with dots at both ends, denoted as AB‾\overline{AB}.

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Ray: A ray is a part of a line that has one fixed starting point (endpoint) and extends endlessly in only one direction. It is represented visually by a straight line with a dot at one end and an arrow at the other, denoted as OP→\overrightarrow{OP}.

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Line: A line is a straight path that extends infinitely in both directions. It has no endpoints and no fixed length. It is shown visually with arrows at both ends to indicate it never stops, denoted as XY↔\overleftrightarrow{XY}.

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Horizontal Lines: These are straight lines that go across from left to right, similar to a 'sleeping' position. They are parallel to the horizon, like the top edge of a blackboard.

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Vertical Lines: These are straight lines that go up and down, similar to a 'standing' position. They are like the side edges of a door or a tall flagpole.

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Slanting (Oblique) Lines: These are straight lines that are neither horizontal nor vertical. They appear tilted or leaning, like a ladder placed against a wall.

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Curved Lines: Unlike straight lines, curved lines change direction and do not follow a straight path. Examples include the shape of a circle, a wavy line, or the path of a snake.

📐Formulae

Line Segment AB=AB‾AB = \overline{AB}

Ray PQ=PQ→PQ = \overrightarrow{PQ}

Line XY=XY↔XY = \overleftrightarrow{XY}

Length of Segment AB=Distance between point A and point BAB = \text{Distance between point } A \text{ and point } B

💡Examples

Problem 1:

Identify the type of line represented by a sunbeam coming from the Sun.

Solution:

  1. The sunbeam starts at a fixed point (the Sun). 2. It travels infinitely in one direction toward the Earth. 3. A figure with one endpoint that extends infinitely in one direction is called a Ray.

Explanation:

Since the light has a starting point but no ending point in space, it is a Ray, denoted as S→\overrightarrow{S} where SS is the Sun.

Problem 2:

How many line segments are used to form a simple triangle?

Solution:

  1. A triangle is a closed shape made of straight sides. 2. Each side connects two corners (vertices). 3. There are 3 sides in a triangle, and each side is a line segment. 4. Total line segments = 33.

Explanation:

A triangle consists of three connected line segments, such as AB‾\overline{AB}, BC‾\overline{BC}, and CA‾\overline{CA}.