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CBSE Class 7 · Mathematics

Parallel and Intersecting Lines

Official NCERT chapter from Ganita Prakash Part I (book code gegp1). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “Parallel and Intersecting Lines” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 7
  • Easy level
  • 8 concepts

1Across the Line

A line that crosses another makes angles at the crossing. “Across the line” means you can name those angles, not that you jumped the line in a story.

Two marks that never meet on the page may still meet if extended — check the extend-test.

Figure. Two lines that cross at P are intersecting lines. They make four angles at that one point. Until P is named, you are staring, not reasoning.

How it works

  1. See two linesThis pair.
  2. Ask if they meet when extendedIntersect, or not.
  3. If they meet, name the angles at the pointAcross the crossing.

2Perpendicular Lines

Perpendicular lines meet at a right angle. A square corner is the test, not a “looks upright” shrug.

A steep slant is not automatically 90°.

Figure. Perpendicular lines meet at a right angle. The small square is the test: it is drawn as a visual square under aspect 1.6 (\Delta x=0.036, \Delta y=0.0576). Looking tidy is not the test.

How it works

  1. Find the meeting pointIf they meet.
  2. Test for a right angleSet-square, or a known square corner.
  3. If it is 90°, call them perpendicularThe name follows the test.

3Between Lines

Between two lines you can ask: do they meet, are they the same distance apart, what angles sit in the gap. “Between” is a place for those questions.

A gap that looks even is not a proof of parallel until a test.

Figure. Parallel lines never meet and stay the same distance apart. The two brackets are the same span d — that equal gap is the test, not that the drawing looks level.

How it works

  1. Name the two linesA pair.
  2. Look at the strip between themThe between.
  3. Ask meet / distance / anglesThe questions.

4Transversals

A transversal is a line that cuts two or more other lines. It creates a family of angles you can name. Without a cut, there is no transversal.

A line that misses both is not a transversal.

Figure. A transversal n cuts parallels l and m and makes eight angles. Number them before you chase a pair. The slant is a true 30^\circ to the parallels under aspect 1.6.

How it works

  1. Draw or see two linesThe pair.
  2. See a third that cuts bothThe transversal.
  3. Name it as the cutterNot a decoration.

5Corresponding Angles

Corresponding angles sit in the same “corner job” at the two crossings: both top-left, for example. If the cut lines are parallel, corresponding angles match.

Any two angles that look similar are not automatically corresponding.

Figure. Corresponding angles sit in the same seat at each crossing — here 2 and 6 are both above the parallel and to the right of the transversal. When l \parallel m, those two are equal.

How it works

  1. Mark the two crossingsTransversal through two lines.
  2. Pick the same corner jobTop-left and top-left.
  3. Those are corresponding; if lines are parallel they are equalThe test.

6Drawing Parallel Lines

To draw a parallel you copy an angle (or use a set-square slide) so corresponding angles match. Freehand “looks parallel” is an illusion until a copy-test.

Two lines that do not meet on a short page may still meet far off the page.

Figure. To draw a parallel through P: send a transversal through P, then copy the corresponding angle so the new line sits in the same seat. The two marks labelled eq are that copied pair. The new line through P then never meets l.

How it works

  1. Copy the angle you needCorresponding match.
  2. Slide or construct so the copy sits at the second crossingThe draw.
  3. Check with a third point if you canNot freehand only.

7Alternate Angles

Alternate angles sit on opposite sides of the transversal, between the pair (interior) or outside. If the pair is parallel, alternate interior angles match.

Alternate is a position-name, not “every other angle you like”.

Figure. Alternate interior angles sit on opposite sides of the transversal and between the parallels — here 4 and 6. When l \parallel m they are equal. They make the Z, not the F of corresponding angles.

How it works

  1. Find the transversalThe cutter.
  2. Find a pair on opposite sides, in the matching bandAlternate.
  3. If the lines are parallel, those interiors are equalThe match.

8Parallel Illusions

Rails in a drawing can look like they meet in the distance. That is an illusion of seeing, not a proof they are not parallel. Parallel is a never-meet-in-the-plane test, not a “looks like”.

A photograph of a road is not a geometry proof.

Figure. Crossing hatch marks can make parallel lines look as if they meet. l and m have the same slope and the same gap d — they are parallel. Trust the equal-distance test, not the illusion.

How it works

  1. Separate look from testThe picture can lie.
  2. Run meet-when-extended or equal-correspondingThe maths.
  3. Call a look-only claim an illusionThis heading.
A transversal is
  1. A line that cuts two or more other lines
  2. Any third mark on the page
  3. A lakh

It must cut.

Notes

  • The official chapter title is “Parallel and Intersecting Lines”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Recap

Hold these pegs from the official chapter “Parallel and Intersecting Lines”. The wording is ExamMaster’s teaching, not a textbook recap.

Across the Line
A line that crosses another makes angles at the crossing.
Perpendicular Lines
Perpendicular lines meet at a right angle.
Between Lines
Between two lines you can ask: do they meet, are they the same distance apart, what angles sit in the gap.
Transversals
A transversal is a line that cuts two or more other lines.
Corresponding Angles
Corresponding angles sit in the same “corner job” at the two crossings: both top-left, for example.
Drawing Parallel Lines
To draw a parallel you copy an angle (or use a set-square slide) so corresponding angles match.

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