Corresponding angles are equal exactly when the lines are parallel

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What to assume they know

A transversal creates two matching sets of four angles: transversal, the two sets of four angles, and which angle corresponds to which
The four angles at a crossing: vertically opposite and linear pairs: linear pairs total 180°, vertically opposite angles are equal
What "parallel" actually claims, and why it is hard to check: the printed definition of parallel, and why looking is not enough
Using a protractor to lay off a stated angle, and copying an angle with tracing paper
Reading a figure in which a mark, not a measurement, records a claim

What they should be able to do

Copy a given angle at a second point on a transversal, and describe what the copy guarantees
State the claim that equal corresponding angles make two lines parallel
State the converse claim, that parallel lines force corresponding angles to be equal
Explain why the two claims are different statements and why both are needed
Predict, and then observe, what happens when you try to make corresponding angles equal on lines that are not parallel
Use one pair of corresponding angles to decide whether two lines are parallel, from given measures
Say in your own words what "necessary and sufficient" means for this pair of claims

Where it usually goes wrong

"Corresponding angles are equal." Only across parallel lines. This is the single most damaging thing a student can carry out of this chapter, and the book guards against it with a whole boxed statement on p.118 saying the opposite for non-parallel lines. Every time the explanation states the equality it must state the condition in the same breath.
"The two boxed claims on p.117 say the same thing twice." They face opposite ways. One takes equal angles and produces parallelism; the other takes parallelism and produces equal angles. Section 11 exists to make that difference audible.
"One pair of equal corresponding angles is not enough — check all four." One pair settles it. Activity 3 builds a parallel pair from a single copied angle, and once the lines are parallel the other three pairs follow.
"Activity 5 is a drawing exercise I failed at." It is a result. The instruction cannot be carried out, and noticing that is the answer. Frame the failure as the finding before the student attempts it, or they will assume their hand was unsteady.
"The tracing paper proves it." Tracing and measuring are evidence, and the chapter has already said on p.108 why evidence of that kind will always be slightly off. What proves it is the pair of claims taken together.
"If the corresponding angles differ by a little, the lines are nearly parallel, which is close enough." Two lines that differ by a fraction of a degree still meet — far off the page, but they meet, and the definition on p.110 admits no "nearly".
"Both corresponding angles sit to one side of the cutting line, so any two angles on that side correspond." Position within the crossing is what matches, not merely the side. Show ∠2 paired with ∠6, then with ∠7, and measure both pairs.

Questions to check understanding

Given one angle at one crossing and the parallelism of the two lines, find its corresponding angle
Given two corresponding angles' measures, decide whether the lines are parallel and justify the verdict
Given one angle and one corresponding angle that are not equal, state what follows
Construct a line through a given point parallel to a given line by copying an angle, and say which claim guarantees the result
Explain why the two statements on p.117 are not the same statement
Say what would have to be true for Activity 5's instruction to be carried out
Items in the Figure it Out on pp.123–125 that supply a measure at one crossing and ask for one at the other are direct tests of this topic

Examples worth working on the board

Activity 3, Figs. 5.15 to 5.18 (Part I, §5.6, pp.115–116). Checked against the printed page. Four small figures in sequence, all with line l drawn horizontal and transversal t running from lower left to upper right. Fig. 5.15: l and t meeting at X. Fig. 5.16: the same, with the angle above l and right of t labelled a = 60°. Fig. 5.17: a second point Y marked on t, below X. Fig. 5.18: a line m drawn through Y with b = 60° in the matching position, so that l and m look parallel. Inputs: the chosen value 60°, its linear-pair partner 120°, and the instruction that only two distinct angles are wanted in the finished figure.
The construction step (Part I, §5.6, p.116). Two ways of copying the angle are printed: trace ∠a onto tracing paper and lay it down at Y, or measure it with a protractor and lay it off.
The three boxed claims (Part I, §5.6, pp.117–118). Each sits in its own tinted box.
- equal corresponding angles ⟹ the lines are parallel (p.117);
- parallel lines ⟹ equal corresponding angles (p.117);
- lines that are not parallel ⟹ corresponding angles can never be equal (p.118). Claim 3 is the contrapositive of claim 1 and adds no new content, but it is printed separately and it is what Activity 5 is evidence for, so give it its own section.
Activity 4 and Fig. 5.19 (Part I, §5.6, p.117). Checked against the printed page. Lines l and m drawn horizontal and parallel, each carrying a single arrow mark, cut by a transversal t; ∠a sits above l on the right of t, and ∠b above m on the right of t. The activity asks the reader to identify the notation that says the lines are parallel, then to trace ∠a and lay it over ∠b.
Activity 5 and Fig. 5.20 (Part I, §5.6, p.117). Checked against the printed page. Two lines l and m drawn one above the other and not parallel — they converge slightly to the left, so the gap between them widens as you go right, and they carry no parallel marks. The reader is told to draw a transversal making one pair of corresponding angles equal, and the page then asks whether they are finding it hard. This is the most important figure in the section and the easiest to mis-draw: if the figure draws them parallel, the activity becomes possible and the argument collapses.
Example 2 (Part I, §5.8, p.121). Inputs: in Fig. 5.27 a transversal t cuts lines l and m; ∠a is 120° and ∠f is 70°. In that figure ∠a and ∠b are the two angles above l, and ∠b and ∠f occupy matching positions at the two crossings.
A caution on Activity 3's status. Activity 3 constructs a parallel pair; it does not by itself prove claim 1, because "they appear to be parallel" is exactly the kind of evidence §5.3 warned against. The chapter is honest about this — it asks whether the lines appear parallel and answers that they do.

Figures to have open

The Activity 3 sequence as one figure that can be shown moving: a line, a transversal, a marked angle, a second point, and a copied angle. It must be able to run forwards and backwards.
A transversal sweeping across a non-parallel pair with both corresponding angles displayed live. The book prints the situation as a still (Fig. 5.20) and asks the reader to attempt it by hand. The moving version is an added contribution and is the thing that makes claim 3 felt rather than asserted.
The single-arrow parallel notation, matching Fig. 5.19 (p.117) and Fig. 5.9 (p.112) — Activity 4 explicitly asks the reader to read that mark.
Fig. 5.27's configuration for section 12, with the angle letters as printed.
Tracing paper, shown as a translucent overlay that can be picked up and moved.
No photograph, table or dataset from the textbook is needed.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 5 "Parallel and Intersecting Lines", §5.6 "Corresponding Angles", pp.115–118 — the naming (p.115), Activity 3 with Figs. 5.15 to 5.18 (p.116), the first boxed claim, Activity 4 with Fig. 5.19, the second boxed claim, and Activity 5 with Fig. 5.20 (p.117), and the third boxed claim (p.118)
Same part, §5.7, Note to the Teacher, p.119, for the phrase that names the two-way property
Same part, §5.8, Example 2 with Fig. 5.27, p.121, for the test applied
Same part, §5.3, p.110, for the definition the test is a test of
Same part, SUMMARY, p.126, fifth bullet, which carries both directions in one bullet