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Geometry - Point, Line, Line Segment, and Ray

Grade 4ICSE

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

🔑Concepts

A Point is an exact location in space represented by a small dot. It has no length, breadth, or thickness. In geometry, points are named using capital letters like AA, BB, or CC. Visually, it is just a tiny dot on a plane.

A Line is a straight path of points that extends infinitely in both directions. It has no endpoints and no fixed length, meaning it cannot be measured. Visually, it is drawn with arrows at both ends, such as XY\overleftrightarrow{XY}, to show it continues forever.

A Line Segment is a part of a line that has two fixed endpoints. Because it has a starting and an ending point, it has a definite length that can be measured using a ruler. Visually, it is shown as a straight path between two points AA and BB, written as AB\overline{AB}.

A Ray is a part of a line that starts at a fixed point (called the initial point) and extends infinitely in only one direction. Visually, it is represented with one endpoint and one arrow, written as OP\overrightarrow{OP} where OO is the starting point.

Horizontal lines are straight lines that run from left to right, similar to the horizon or the sleeping position. Vertical lines are straight lines that run up and down, standing tall like a pillar.

Slanting or Oblique lines are lines that are neither horizontal nor vertical. They lean at an angle, like a ladder placed against a wall.

Parallel lines are lines that stay the same distance apart and never meet, no matter how far they are extended. Visually, they look like the tracks of a railway line. Intersecting lines are lines that cross each other at a single common point, appearing like the letter XX.

📐Formulae

Symbol for a Line: AB\overleftrightarrow{AB}

Symbol for a Line Segment: AB\overline{AB}

Symbol for a Ray starting at A: AB\overrightarrow{AB}

Number of endpoints in a Line Segment = 22

Number of endpoints in a Ray = 11

Number of endpoints in a Line = 00

💡Examples

Problem 1:

Identify the following: (a) A figure with one endpoint that extends infinitely in one direction. (b) A figure with two endpoints PP and QQ measuring 77 cm.

Solution:

(a) Ray; (b) Line Segment PQ\overline{PQ}.

Explanation:

A figure starting at a point and continuing forever is a ray. A figure with two fixed endpoints that can be measured is a line segment.

Problem 2:

In a rectangle ABCDABCD, identify the relationship between the top side ABAB and the bottom side DCDC, and the relationship between side ABAB and side BCBC.

Solution:

ABAB and DCDC are parallel lines (\|); ABAB and BCBC are intersecting lines.

Explanation:

Opposite sides of a rectangle never meet, making them parallel. Adjacent sides meet at a corner (vertex), making them intersecting lines.