A transversal creates two matching sets of four angles

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What to assume they know

The four angles at a crossing: vertically opposite and linear pairs: two crossing lines make four angles, in at most two sizes; linear pairs total 180°; vertically opposite angles are equal
What "parallel" actually claims, and why it is hard to check: what parallel claims, and why the eye cannot settle it
Numbering the parts of a figure and keeping the numbering straight while reasoning about it
Counting pairs from a small set without double-counting

What they should be able to do

Define a transversal, and identify one in a figure
State how many angles are formed when a transversal crosses two lines
Count the pairs of vertically opposite angles in that figure, and say why there are exactly four
Argue that at most four distinct angle measures can appear among the eight
Explain why exactly five distinct measures is impossible among a named subset
Split the eight angles into the two sets the transversal makes, one at each crossing
Match an angle in one set with the angle occupying the same position in the other, and name that relation
Say what is still unproved at the end of the section

Where it usually goes wrong

"A transversal has to be perpendicular to the two lines, or has to be slanted." It only has to cut across both. Fig. 5.14 shows a slanted one; in §5.7 (p.118) the transversal is at 90° to both lines, and it is still a transversal.
"A transversal only makes sense for parallel lines." §5.5 introduces it for two lines with no parallelism assumed, and Fig. 5.14 does not draw them parallel. Checked against p.115. If the explanation assumes parallelism here, §5.6 has nothing left to prove.
"Eight angles, so eight things to learn." Four of them are copies. The section is a counting argument, not a naming exercise.
"Corresponding angles are the ones that are equal." Not yet. In §5.5 and at the opening of §5.6 they are only the ones in matching positions. Their equality is the next topic, and it is conditional.
"The two crossings could have completely unrelated angles." They could, so far — and that is exactly the honest state of play at the end of this topic. Section 11 should say so out loud rather than hint at the answer.
"Corresponding just means both angles sit to one side of both lines." It means the same position within each crossing: one side of the transversal and one side of its own line, matched on both counts. Show a wrong pairing beside a right one.

Questions to check understanding

Identify the transversal in a three-line figure and say which two lines it cuts
State how many angles a transversal makes with a pair of lines
List every vertically opposite pair in a numbered figure, and say how many there are
Say the largest number of different measures the eight angles can have, and justify it
Given a named subset of the eight, decide whether they can all be different
Given one angle number, name its corresponding angle in the other set
Distinguish, in a figure, a correctly matched corresponding pair from a plausible-looking wrong one
Later multi-step items — Fig. 5.30 and Fig. 5.31, pp.123–124 — all begin by locating the transversal, so this is examined indirectly throughout

Examples worth working on the board

Fig. 5.14 (Part I, §5.5, p.115). Checked against the printed page. Two lines l and m run from lower left to upper right, one above the other, and a steeper line t cuts down through both. The eight angles are numbered so that at the upper crossing 1 is upper left, 2 upper right, 4 lower left, 3 lower right; at the lower crossing 5 is upper left, 6 upper right, 8 lower left, 7 lower right. Neither l nor m carries a parallel mark, and the two are not drawn parallel. The numbering is essential and it is drawn, not typed — it must be redrawn exactly, because §5.6 and §5.8 both refer back to it.
The two counting questions (Part I, §5.5, p.115). First: can all eight measures be different? Second: can five of them be different, taking the specific list ∠6, ∠5, ∠4, ∠3, ∠2? Checked against p.115: the page asks both, then closes the section by stating a ceiling of four distinct angle measures — which settles the first question and forces the second, though the second is never taken up by name.
The vertically opposite count (Part I, §5.5, p.115). Input: ∠1 and ∠3 are vertically opposite, so they are equal. There are four such pairs across the two crossings — with the numbering above they are 1-3, 2-4, 5-7 and 6-8. From that the printed conclusion follows: the eight angles carry at most four different measures.
Why five is impossible (not in the book). The named list contains both ∠2 and ∠4, and those two are a vertically opposite pair, so two of the five are forced equal. The chapter poses the question and leaves the reasoning to the reader; the solutions appendix bound after the chapter records the same argument. Present it as the reader's work, which is what it is.
A second route to the ceiling, which the chapter does not state (not in the book). Each crossing on its own already has at most two distinct measures, from the previous topic. Two crossings therefore give at most four — which is a second route to the printed ceiling, and a better one, because it shows where the four comes from. Badge it as the explanation's route.
The two sets (Part I, §5.6, p.115). The transversal makes one group of four angles with l and another group of four with m. The printed pairing is ∠1 with ∠5, ∠2 with ∠6, ∠3 with ∠7, ∠4 with ∠8.

Figures to have open

Fig. 5.14 redrawn, with the printed numbering 1 to 8 in the printed positions. The rest of the chapter refers back to this arrangement, so it must match. It should also be able to show: the transversal sliding, and one crossing translating along the transversal onto the other.
A version of the same figure in which l and m are visibly not parallel, for sections 4 to 8, and a second in which they are, for section 10 onwards. The contrast is the argument.
No photograph, table or dataset from the textbook is needed for this topic.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 5 "Parallel and Intersecting Lines", §5.5 "Transversals", p.115 — the whole section, including Fig. 5.14, the two counting questions and the printed conclusion about the maximum number of distinct measures
Same part, §5.6 "Corresponding Angles", p.115, for the two sets and the naming of corresponding angles; the equality results that follow on pp.116–118 belong to Corresponding angles are equal exactly when the lines are parallel
Same part, §5.1, pp.107–108, for the vertically opposite result the count leans on
Same part, p.114, for the sentence that motivates transversals
Same part, SUMMARY, p.126, fourth bullet