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Geometry - Lines, Line Segments, and Rays

Grade 5ICSE

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

🔑Concepts

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A point represents a specific location in space and has no dimensions (length, breadth, or thickness). It is represented by a dot and named with a capital letter.

A single dot representing point P.
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A line segment is a part of a line with two fixed endpoints. It has a definite length and can be measured.

A line segment AB with two distinct endpoints.
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A ray is a part of a line that starts at one fixed point and extends infinitely in one direction. It has no definite length.

A ray XY starting at point X and passing through Y with an arrowhead.
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A line extends infinitely in both directions. It has no endpoints and no definite length.

A line L with arrowheads on both ends showing infinite extension.
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Parallel lines are lines on a flat surface that never meet, no matter how far they are extended. They always maintain a constant distance from each other.

Two horizontal parallel lines m and n.

📐Formulae

Length of Segment AB=∣A−B∣\text{Length of Segment } AB = |A - B|

Number of lines passing through one point=Infinite\text{Number of lines passing through one point} = \text{Infinite}

Number of lines passing through two distinct points=1\text{Number of lines passing through two distinct points} = 1

Angle of intersection for AB⊥CD=90∘\text{Angle of intersection for } AB \perp CD = 90^\circ

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

Symbol for Line Segment: AB‾\text{Symbol for Line Segment: } \overline{AB}

Symbol for Ray: AB→\text{Symbol for Ray: } \overrightarrow{AB}

💡Examples

Problem 1:

A line segment XY‾\overline{XY} is 12 cm12\text{ cm} long. A point ZZ lies on the segment such that the length of XZ‾\overline{XZ} is 7 cm7\text{ cm}. Find the length of the segment ZY‾\overline{ZY}.

Solution:

  1. We know that the total length of the segment is XY=12 cmXY = 12\text{ cm}.
  2. The segment is divided into two parts: XZXZ and ZYZY.
  3. Therefore, XY=XZ+ZYXY = XZ + ZY.
  4. Substituting the known values: 12 cm=7 cm+ZY12\text{ cm} = 7\text{ cm} + ZY.
  5. To find ZYZY, subtract 77 from 1212: ZY=12 cm−7 cm=5 cmZY = 12\text{ cm} - 7\text{ cm} = 5\text{ cm}.

Explanation:

This problem uses the property that the total length of a line segment is the sum of its parts when a point lies between the endpoints.

Problem 2:

Identify the following geometric figures: (i) A figure with two endpoints, (ii) A figure with one endpoint and one arrowhead, (iii) A figure with arrowheads at both ends.

Solution:

i. A figure with two fixed endpoints is a Line Segment, denoted as AB‾\overline{AB}.\nii. A figure with one fixed endpoint and one arrowhead (extending infinitely) is a Ray, denoted as AB→\overrightarrow{AB}.\niii. A figure with arrowheads at both ends (extending infinitely in both directions) is a Line, denoted as AB↔\overleftrightarrow{AB}.

Explanation:

This example tests the conceptual understanding of the physical characteristics and symbolic representations of lines, segments, and rays.

Problem 3:

In the given figure, point MM is the midpoint of the line segment PQ‾\overline{PQ}. If the length of PM‾=5.5 cm\overline{PM} = 5.5\text{ cm}, what is the total length of the segment PQ‾\overline{PQ}?

Line segment PQ with midpoint M and segment PM labeled 5.5 cm.

Solution:

PQ=PM+MQPQ = PM + MQ Since MM is the midpoint, PM=MQ=5.5 cmPM = MQ = 5.5\text{ cm}. PQ=5.5 cm+5.5 cm=11 cmPQ = 5.5\text{ cm} + 5.5\text{ cm} = 11\text{ cm}

Explanation:

A midpoint divides a line segment into two equal parts. To find the total length, we multiply the length of one part by 2 or add the two equal parts together.

Problem 4:

Observe the figure below. Name the intersecting lines and their point of intersection.

Two lines AB and CD crossing at point O.

Solution:

The intersecting lines are AB↔\overleftrightarrow{AB} and CD↔\overleftrightarrow{CD}. The point of intersection is OO.

Explanation:

Intersecting lines are two lines that cross each other at exactly one common point, known as the point of intersection.

Lines, Line Segments, and Rays Class 5 Notes & Examples