What "parallel" actually claims, and why it is hard to check

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What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

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What to assume they know

The four angles at a crossing: vertically opposite and linear pairs: what it means for two lines to intersect, and the four angles a crossing makes
Perpendicular lines as the case where all four are equal: perpendicular lines, and the square corner mark
A line as unending in both directions, drawn as a segment with arrowheads
Line segment, endpoint and midpoint from Class 6
Reading a dot grid: locating points and joining them with straight segments

What they should be able to do

State both conditions in the definition of parallel lines — same plane, and never meeting however far extended
Give a counter-example to "never meet, therefore parallel" using two lines on different surfaces
Describe how two line segments meet, using the words for a point, an endpoint and a midpoint, and give the angle where one is marked
Decide, for a pair of segments drawn short, whether extending them would make them meet, and say what the decision rests on
Identify pairs of parallel lines in a dot-grid figure and mark them with the arrow notation
Draw a segment parallel to a given one on dot paper, and say which orientations are hardest
Explain why eye judgement is not a proof of parallelism, and name what the chapter reaches for instead

Where it usually goes wrong

"They do not meet on my page, so they are parallel." The page is finite and the claim is not. Section 3 should show a pair that separates by a millimetre over a page and meets a hundred pages away.
"Never meeting is the whole definition." It is half of it. Two lines on different flat surfaces can miss each other for ever without being parallel — the printed teacher's note gives exactly this case. Checked against p.110.
"Parallel means equally far apart, so measure the gap in two places." Two places is not enough, and in any case the chapter's own definition is about meeting, not spacing. The distance test is a good instinct that the section deliberately does not licence.
"Parallel lines must run across or up the page." Fig. 5.6 and Fig. 5.12 are built out of diagonals precisely to break this, and the teacher's note on p.114 says the awkward slopes are the point.
"Railway lines meet at the horizon, so they are not really parallel." The keyboard photograph on p.110 has the same effect. Perspective is a fact about the picture, not about the lines — hold this one back for Parallel illusions: why the eye is not a proof, where the chapter makes it the closing argument.
"If two segments do not cross, the lines they lie on do not cross." A segment is a piece of a line, so two segments failing to touch settles nothing about the lines they sit on. ST and UV are the pair Fig. 5.5 draws with a narrowing gap, and whether extending them brings them together is exactly the question the page leaves open.

Questions to check understanding

Complete the definition of parallel lines, both conditions
Given two lines that never meet, decide whether they are parallel and justify
Describe how two named segments in a figure meet, using the printed vocabulary and giving the angle
Say whether a pair of segments would meet if extended, and on which side
Mark the parallel sets in a figure with single and double arrows, and the perpendicular pairs with the square symbol (the printed task on p.113)
Draw a segment parallel to a given one on dot paper, and describe the method
Given three segments, decide which two are parallel and state what your decision rests on (the printed task at Fig. 5.13, p.114)
Explain why looking is not enough, in one or two sentences

Examples worth working on the board

Fig. 5.5 (Part I, p.109). Checked against the printed page. Five separate configurations of labelled segments scattered on one field, every endpoint drawn as a filled dot: segments OP and QR lying near each other and running the same way, with the gap between them all but unchanged from one end to the other; segments ST and UV also close together and running the same way, but drawn so that the gap between them visibly narrows towards the right; segments AB and CD crossing at a point marked X; segments IJ and LM crossing at a point marked Y; and segments FG and FH sharing the endpoint F, with the angle between them marked 115.3°. The chapter uses FG and FH as its worked example of how to describe a meeting.
The two extension questions (Part I, §5.3, p.109). Would ST and UV meet if extended? Would OP and QR? These are asked and not answered on the page. Show the extension showing and stopping at the edge of the paper.
The photographs (Part I, §5.3, p.110). Checked against the printed page. Three small photographs across the top of the page — a piano keyboard seen at an angle, a slatted bench, and a run of upright bars — and below the definition, two artwork panels: a white interlaced star pattern on brown, and a yellow-and-purple herringbone panel. Redraw or re-shoot; these are the book's own images. Note that in the keyboard photograph the parallel edges are drawn towards a vanishing point by perspective, which is itself worth a sentence in section 4.
The definition (Part I, §5.3, p.110). Set in its own tinted box. Two conditions: the lines lie on one plane, and they do not meet however far either is extended in either direction. Both conditions must appear when explaining it.
The teacher's note (Part I, §5.3, p.110). One ruled mark across a desk top and another across the blackboard can miss each other for ever and still fail the definition, because they are not on one flat surface. This is the cleanest counter-example available, and the chapter prints it as a note to the teacher rather than in the student text — so it is easily skipped, and it should not be.
Fig. 5.6 (Part I, p.110). Checked against the printed page. A rectangular field of dots carrying nine drawn segments lettered a to i, at mixed orientations — some vertical, some horizontal, several diagonal at different slopes. The printed question asks which pairs appear to be parallel.
Fig. 5.12 and Fig. 5.13 (Part I, p.114). Checked against the printed page. Fig. 5.12 is a dot grid carrying eight segments lettered a to h, and asks the reader to draw a parallel to each; the teacher's note on the same page says that horizontal, vertical and 45° segments are easy and other slopes are not. Fig. 5.13 shows a segment a on the left and two segments b and c fanning from one shared point on the right, drawn at slopes so close that the eye cannot separate them, plus a fourth segment joining a's lower endpoint to that shared point. The reader must say which of b and c is parallel to a, and how they decided. Do not state the answer in the explanation: the whole function of this figure is to be undecidable by eye, and §5.6 supplies the method.
Where §5.4 fits (Part I, pp.111–112). The numbered section between the definition and the notations is a paper-folding activity with blanks to fill in. It is handled as its own topic, Parallel and Perpendicular Lines in Paper Folding, and is marked as an activity rather than an explanation. This topic should mention only its result: the opposite edges of a sheet are parallel, the adjacent edges are perpendicular, and each fold in half produces more parallels than the last.

Figures to have open

Fig. 5.5 redrawn: five configurations of labelled segments with dotted endpoints, including one shared-endpoint pair carrying a printed angle. Standard schematic, but the labels must match the printed ones so a student can follow along in the book.
Two intersecting planes in three-quarter view, each carrying one line. This is the one figure the topic cannot be taught without, and the chapter does not print it — the same-plane condition is stated in words only. It must be built.
A dot grid that can carry drawn segments at arbitrary slopes, reused for sections 8, 10 and 11.
The parallel arrow notation, single and double, and the square corner, matching Fig. 5.9 (p.112).
Photographs or clean redraws of everyday parallels — keyboard, bench, bars. Redraw rather than reproduce; the printed images are the book's own.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 5 "Parallel and Intersecting Lines", §5.3 "Between Lines", pp.109–110 — Fig. 5.5 and the meeting vocabulary and the two extension questions (p.109), the photographs, the definition box, the classroom prompt, the artwork, Fig. 5.6 and the Note to the Teacher (p.110)
Same part, §5.4 "Parallel and Perpendicular Lines in Paper Folding", pp.111–112, referenced only for its result; the activity itself is Parallel and Perpendicular Lines in Paper Folding
Same part, the unnumbered block "Notations", p.112, for the arrow marks
Same part, the unnumbered Figure it Out that follows it, pp.113–114 — Fig. 5.10 and Fig. 5.11 (p.113), Fig. 5.12 and Fig. 5.13 and the closing sentence that reaches for transversals (p.114)
Same part, §5.5, p.115, for the word the section closes by promising
Same part, SUMMARY, p.126, third bullet