This MCQ module is based on: 5.3 Parallel Lines
TOPIC 17 OF 31
5.3 Parallel Lines
🎓 Class 7
Mathematics
CBSE
Theory
Ch 5 — Parallel and Intersecting Lines
⏱ ~15 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: 5.3 Parallel Lines
Targeting Class 7 level in Geometry, with Basic difficulty.
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5.3 Parallel Lines
Look around you — the two rails of a railway track, the opposite edges of a ruler, the lines on a ruled notebook, the rungs of a ladder, the strings of a piano. What is common to the lines in these pictures? They do not seem likely to intersect each other. Such lines are called parallel lines?.
Definition — Parallel Lines
Parallel lines are a pair of lines that lie on the same plane, and do not meet however far we extend them at both ends. We write \(l \parallel m\) to mean "line \(l\) is parallel to line \(m\)".
The arrow marks on the lines in the figure above are a standard notation used to indicate that the two lines are parallel. Parallel lines are often also used in artwork and shading.
Spotting Parallel Lines
Name some parallel lines you can spot in your classroom.
Examples: opposite edges of the blackboard, two long sides of a door frame, opposite borders of your notebook, the parallel stripes on a shirt, the lines on ruled paper.
Examples: opposite edges of the blackboard, two long sides of a door frame, opposite borders of your notebook, the parallel stripes on a shirt, the lines on ruled paper.
Note to the Teacher: It is important that the lines lie on the same plane. A line drawn on a table and a line drawn on the board may never meet but that does not make them parallel.
Figure it Out — Fig. 5.6 (Spotting Parallels)
Which pairs of lines appear to be parallel in the given dotted grid with diagonal line segments (Fig. 5.6)?
Line segments that have the same slope on the grid (i.e., rise-over-run is identical) are parallel. Typically, segments of matching "slant" — for example two segments each going 2 dots right and 1 dot down — are a parallel pair. Count the grid steps to check.
Figure it Out — Page 113
Q1. Draw some lines perpendicular to the lines given on the dot paper (Fig. 5.10).
For a horizontal segment, a perpendicular is any vertical segment. For a diagonal going 1-right 1-up (slope +1), a perpendicular segment goes 1-right 1-down (slope −1). On dot-paper, swap rise and run and flip one sign to get the perpendicular direction. Mark the right-angle with a small square.
Q2. In Fig. 5.11, mark the parallel lines using the notation (single arrow, double arrow, etc.). Mark the angle between perpendicular lines with a square symbol. (a) How did you spot the perpendicular lines? (b) How did you spot the parallel lines?
(a) Perpendicular: On the square grid, any horizontal segment meets any vertical segment at 90°. A diagonal of slope +1 is perpendicular to a diagonal of slope −1.
(b) Parallel: Segments with identical slope (same rise/run on the grid) are parallel. Mark each family of parallels with matching arrow-counts (single, double, triple arrowheads).
(b) Parallel: Segments with identical slope (same rise/run on the grid) are parallel. Mark each family of parallels with matching arrow-counts (single, double, triple arrowheads).
Q3. On dot paper, draw different sets of parallel lines. The line segments can be of different lengths but should have endpoints at dots.
Choose a direction vector, e.g., (3 right, 2 up). From different starting dots, draw segments with the same (3,2) displacement — all are parallel. Repeat with different direction vectors to create multiple parallel families.
Perpendicular and Parallel Lines Around Us
Perpendicular and parallel lines appear in many everyday objects and spaces:
- Railway tracks — two long parallel rails joined by perpendicular sleepers.
- Graph paper or square-ruled notebooks — two families of parallel lines meeting at right angles.
- Brick walls and tiled floors — rows and columns.
- Books, TV screens, windows — rectangular shapes bounded by pairs of parallel sides.
- Pedestrian "zebra" crossings on roads — equally-spaced parallel white bands.
Activity 2 — Perpendicular and Parallel Folds (Page 112)
Activity 2: Paper Folding to Create Parallels & Perpendiculars
L3 ApplyMaterials: Square sheet of paper.
Predict: Can three folds on a square sheet give you both parallel and perpendicular lines at once?
- Fold the square in half horizontally and open it — call the crease line \(p\).
- Fold the top and bottom edges to meet the crease \(p\) — two new horizontal creases appear.
- Open the sheet. Observe the three horizontal creases and the original edges.
- Now fold the sheet in half vertically, then fold the left and right edges to meet that crease. Open.
Observations:
- The three horizontal creases are all parallel to each other and to the top/bottom edges.
- The three vertical creases are parallel to each other.
- Every horizontal crease is perpendicular to every vertical crease.
Why? Folding the edge onto a line produces a crease perpendicular to the line. Folding the line onto itself gives a crease at the midline, parallel to the original edge.
Activity — Paper Folding Challenge (Fig. 5.8 on Page 112)
Take a square sheet of paper. Fold it in the middle and unfold it. Fold the edges towards the centre line and unfold. Fold the top right and bottom left corners onto the creased line to create triangles. Refer to Fig. 5.8. The triangles should not cross the crease lines. Are \(a, b,\) and \(c\) parallel to \(p, q\) and \(r\) respectively? Why or why not?
Answer:
- Line segments \(a, b\) and \(c\) are parallel to line segments \(p, q\) and \(r\) respectively.
- \(a\) and \(p\) are on parallel lines. \(b, q\) are both perpendicular to these creases, so are parallel to each other.
- \(c, r\) are both parallel lines because the triangular folds create lines parallel to the same diagonal.
Vertical & Diagonal Folds
When you make a new vertical line after a horizontal fold, the vertical is perpendicular to the horizontal creases. A diagonal fold can also create lines parallel to earlier diagonals.
Competency-Based Questions
Scenario: A city planner is sketching a neighbourhood grid. Roads running East–West are labelled \(E_1, E_2, E_3\) and roads running North–South are labelled \(N_1, N_2, N_3\). Every east-road is drawn using a single ruler setting and every north-road using a different ruler setting, both rulers held perfectly straight.
Q1. Which roads are parallel to each other, and which are perpendicular?
L3 Apply\(E_1 \parallel E_2 \parallel E_3\) (all E–W). \(N_1 \parallel N_2 \parallel N_3\) (all N–S). Every \(E_i \perp N_j\) because East–West is at 90° to North–South.
Q2. A delivery van driver claims that because \(E_1 \parallel E_2\) and \(E_2 \parallel E_3\), she can use the same turning manoeuvre at every crossing. Analyse her reasoning.
L4 AnalyseCorrect analysis: Parallel lines have the same direction. Since every E-road has the same direction, and every N-road has the same direction, every crossing forms the same set of angles (four 90° angles). So the same manoeuvre works at each crossing.
Q3. A second planner argues: "If I add a diagonal road \(D\) that crosses \(E_1\) at 60°, then \(D\) also crosses \(E_2\) at 60°." Evaluate.
L5 EvaluateTrue. Because \(E_1 \parallel E_2\), a transversal cuts them at equal corresponding angles. So if \(D\) makes 60° with \(E_1\), it makes 60° with \(E_2\). (This is the corresponding-angles property we will develop in Section 5.6.)
Q4. Design a mini-map of four roads such that exactly one pair is parallel and exactly one pair is perpendicular. Describe angles.
L6 CreateSample: Roads \(A\) and \(B\) horizontal and parallel. Road \(C\) vertical (perpendicular to \(A\), and also to \(B\), but we only need one pair, so let's modify). Alternative — \(A\parallel B\) horizontal, \(C\) diagonal at 40° crossing both, \(D\) perpendicular only to \(C\). Many valid designs exist.
Assertion–Reason Questions
Assertion (A): Two lines drawn on the same plane that never meet are parallel.
Reason (R): Parallel lines are defined as two lines in the same plane that do not intersect even when extended.
Reason (R): Parallel lines are defined as two lines in the same plane that do not intersect even when extended.
Answer: (a). R is the definition of A.
Assertion (A): A line on the ceiling and a line on the floor that never meet are always parallel.
Reason (R): Two non-intersecting lines are parallel only when they lie in the same plane.
Reason (R): Two non-intersecting lines are parallel only when they lie in the same plane.
Answer: (d). A is false — ceiling and floor are different planes, so such lines are skew, not parallel. R is true and explains why A is false.
Frequently Asked Questions — Parallel and Intersecting Lines
What is Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool in NCERT Class 7 Mathematics?
Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool is a key concept covered in NCERT Class 7 Mathematics, Chapter 5: Parallel and Intersecting Lines. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool step by step?
To solve problems on Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 5: Parallel and Intersecting Lines?
The essential formulas of Chapter 5 (Parallel and Intersecting Lines) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool important for the Class 7 board exam?
Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool?
Common mistakes in Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool?
End-of-chapter NCERT exercises for Part 2 — Parallel Lines and Perpendicular Lines Around Us | Class 7 Maths Ch 5 | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 5, and solve at least one previous-year board paper to consolidate your understanding.
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