5. Parallel and Intersecting Lines

8 topics1 h

Chapter 5 of NCERT Mathematics for Class 7: Parallel and Intersecting Lines. Six sections — Two lines that meet, Two lines that never meet, The transversal and its corresponding angles, Drawing parallels, The other angle pairs at a transversal and Mistrusting your eyes. Eight videos, 1 h in all.

Worked answers to the 13 exercise questions in this chapter →

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Part 1

Two lines that meet

9 minThe four angles at a crossing: vertically opposite and linear pairsTwo lines cross and four angles open out. How many different sizes can those four be? Four is the obvious answer and it is wrong.9 min · 11 partsहिंदी9 minPerpendicular lines as the case where all four are equalPerpendicular is not a fact about which way two lines point. It is the one crossing where the four angles stop coming in two sizes.9 min · 12 partsहिंदी

Part 2

Two lines that never meet

9 minWhat "parallel" actually claims, and why it is hard to check“Parallel” is a claim about what happens for ever, made from a drawing eight centimetres long. That gap is the whole difficulty.9 min · 12 partsहिंदी

Part 3

The transversal and its corresponding angles

9 minA transversal creates two matching sets of four anglesEight angles look like eight facts to memorise. Draw a third line across two others and it invents nothing new at all.9 min · 12 partsहिंदी9 minCorresponding angles are equal exactly when the lines are parallelThis is the hinge of the chapter, and the shape matters more than the content: there are two statements here, facing opposite ways.9 min · 12 partsहिंदी

Part 4

Drawing parallels

9 minDrawing a parallel line using the corresponding-angle testA construction is only worth something if it carries its own guarantee. Both methods here carry the same one.9 min · 12 partsहिंदी

Part 5

The other angle pairs at a transversal

9 minAlternate angles, and interior angles that add to 180°Nothing new is assumed in this topic, and that is the whole video. Every result is manufactured out of two facts you already own.9 min · 12 partsहिंदी

Part 6

Mistrusting your eyes

9 minParallel illusions: why the eye is not a proofThis topic attacks its own evidence. Every earlier step asked whether two lines look parallel — and the eye can be made to lie.9 min · 12 partsहिंदी

What you will be able to do

  • State how many angles two intersecting lines form, and how many different measures those angles can have
  • State the condition that makes two intersecting lines perpendicular
  • State both conditions in the definition of parallel lines — same plane, and never meeting however far extended
  • Define a transversal, and identify one in a figure
  • Copy a given angle at a second point on a transversal, and describe what the copy guarantees
  • Draw two parallel lines using a straight edge and a set square, and name the line that acts as the transversal
  • Identify the alternate angle of a named angle in a transversal figure
  • State what an illusion of parallelism is, and give an example of one

What this chapter assumes you already know

  • An angle as an amount of turning, measured in degrees, and reading a protractor
  • A straight line makes 180° at any point on it (the straight angle)
  • Two numbers that add to a fixed total: if one goes up the other goes down
  • The habit of labelling parts of a figure with letters so they can be argued about
  • The straight angle: 180° along any line
  • Solving a one-step equation of the form 2x = 180
  • Recognising a right angle and its corner symbol from earlier classes
  • Handling a set square and a ruler (used from §5.7 onwards, previewed here)

It builds directly on A letter-number stands for any number, not one number.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "Vertically opposite means one is above the other."
  • "Four angles, so four different sizes."
  • "The pattern is true because I measured four pairs and it worked."
  • "My protractor said 179°, so the rule is only roughly true."
  • "If two of these four are equal, the lines must be perpendicular."
  • "Linear pairs add to 180° because the book says so."
  • "Perpendicular means one line across and one line up."
  • "You need to measure 90° to make a perpendicular."