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Geometry - Point, Line, Line Segment, and Ray

Grade 3ICSE

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

🔑Concepts

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A Point is a tiny dot that represents a specific location in space. It has no length, breadth, or thickness. In geometry, we name a point using a capital letter, such as Point AA. Visually, it appears as a single small dot on a flat surface.

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A Line is a straight path that extends infinitely in both directions. It has no endpoints and no fixed length. To show it continues forever, we draw arrows at both ends, like XY↔\overleftrightarrow{XY}. A line is straight and can be thought of as an endless string.

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A Line Segment is a part of a line that has two fixed endpoints. Because it has a start and an end, its length can be measured using a ruler. It is represented visually as a straight line with two dots at the ends and is written as PQ‾\overline{PQ}.

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A Ray is a part of a line that starts at one fixed point (the endpoint) and goes on forever in the other direction. Think of a sunbeam starting from the sun. It is drawn with one dot and one arrow at the other end, represented as MN→\overrightarrow{MN}.

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Horizontal Lines are lines that go straight across from left to right, parallel to the ground. They are often called 'sleeping' lines because they lie flat like the horizon.

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Vertical Lines are lines that go straight up and down. They are often called 'standing' lines, similar to the position of a standing person or a vertical flagpole.

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Slanting Lines, also known as oblique lines, are tilted. They are neither horizontal nor vertical. Imagine a ladder leaning against a wall or the slanted side of a mountain.

📐Formulae

Symbol for Point=A\text{Symbol for Point} = A

Symbol for Line=AB↔\text{Symbol for Line} = \overleftrightarrow{AB}

Symbol for Line Segment=CD‾\text{Symbol for Line Segment} = \overline{CD}

Symbol for Ray=EF→\text{Symbol for Ray} = \overrightarrow{EF}

Endpoints of a Line=0\text{Endpoints of a Line} = 0

Endpoints of a Line Segment=2\text{Endpoints of a Line Segment} = 2

Endpoints of a Ray=1\text{Endpoints of a Ray} = 1

💡Examples

Problem 1:

Identify the following figures: (a) A figure with two endpoints XX and YY, (b) A figure that starts at OO and has an arrow at PP.

Solution:

(a) XY‾\overline{XY} is a Line Segment. (b) OP→\overrightarrow{OP} is a Ray.

Explanation:

A figure with two fixed ends is a line segment because it has a measurable distance. A figure with one starting point and one arrow is a ray because it extends infinitely in one direction.

Problem 2:

How many line segments are required to draw a simple triangle with vertices LL, MM, and NN?

Solution:

There are 33 line segments: LM‾\overline{LM}, MN‾\overline{MN}, and NL‾\overline{NL}.

Explanation:

A triangle is a closed shape made of three straight sides. Each side connects two points (vertices), making each side a line segment.