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Lines and Angles - Line

Grade 6CBSE

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

🔑Concepts

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A point is a position in space represented by a fine dot. It has no length, breadth, or thickness. Points are usually denoted by capital letters like PP, QQ, or AA.

A small dot representing point P
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A line is a collection of points that extends infinitely in both directions. It has no endpoints and no definite length. It is denoted as AB↔\overleftrightarrow{AB} or by a small letter like ll.

A line AB with arrows at both ends indicating it extends infinitely.
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A line segment is a part of a line with two fixed endpoints. It has a definite length that can be measured. It is denoted as AB‾\overline{AB}.

A line segment AB with two endpoints.
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A ray is a part of a line that starts at one point (the initial point) and goes infinitely in one direction. It is denoted as OA→\overrightarrow{OA}.

A ray starting at O and passing through A.
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Intersecting lines are two lines that meet at exactly one point. This point is called the point of intersection. Parallel lines are lines in the same plane that never meet, no matter how far they are extended.

Diagram showing intersecting lines on the left and parallel lines on the right.

📐Formulae

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

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

Ray: OA→\text{Ray: } \overrightarrow{OA}

Parallel Lines: l∥m\text{Parallel Lines: } l \parallel m

💡Examples

Problem 1:

How many lines can pass through (i) one given point PP, and (ii) two given points PP and QQ?

Solution:

(i) An infinite number of lines can pass through a single point PP. (ii) Exactly one unique line can pass through two distinct points PP and QQ.

Explanation:

From a single point, we can draw lines in every possible direction. However, to fix a specific straight path, we need at least two distinct points.

Problem 2:

Name the line segments shown in a triangle with vertices XX, YY, and ZZ.

Solution:

The line segments are XY‾\overline{XY}, YZ‾\overline{YZ}, and ZX‾\overline{ZX}.

Explanation:

A triangle is formed by three line segments joining three non-collinear points. Each side is a line segment with two endpoints.

Problem 3:

If the length of segment AB‾=5 cm\overline{AB} = 5\text{ cm} and segment BC‾=3 cm\overline{BC} = 3\text{ cm}, and BB lies between AA and CC on a straight line, find the length of AC‾\overline{AC}.

Solution:

Length of AC‾=AB‾+BC‾\overline{AC} = \overline{AB} + \overline{BC} 5+38\begin{array}{r} 5 \\ + 3 \\ \hline 8 \end{array} Length of AC‾=8 cm\overline{AC} = 8\text{ cm}.

Explanation:

Since the points are collinear and BB is between AA and CC, the total length of the segment is the sum of the individual parts.

Problem 4:

Identify and name all the pairs of intersecting lines shown in the quadrilateral ABCDABCD with diagonals ACAC and BDBD intersecting at OO.

A quadrilateral ABCD with diagonals AC and BD intersecting at point O.

Solution:

The pairs of intersecting lines (or line segments) are:

  1. AB‾\overline{AB} and BC‾\overline{BC} at point BB.
  2. BC‾\overline{BC} and CD‾\overline{CD} at point CC.
  3. CD‾\overline{CD} and DA‾\overline{DA} at point DD.
  4. DA‾\overline{DA} and AB‾\overline{AB} at point AA.
  5. AC‾\overline{AC} and BD‾\overline{BD} at point OO.

Explanation:

Any two lines that cross each other at a single point are called intersecting lines. In a quadrilateral with diagonals, the sides meet at vertices and the diagonals meet each other inside the figure.

Problem 5:

In the given figure, three lines ll, mm, and nn are parallel. If a transversal line pp intersects them, name the points of intersection.

Three horizontal parallel lines l, m, n intersected by a slanting transversal line p at points X, Y, and Z.

Solution:

The points of intersection of line pp with lines ll, mm, and nn are points XX, YY, and ZZ respectively.

Explanation:

A line that intersects two or more lines at distinct points is called a transversal. Here, pp is the transversal intersecting the three parallel lines.