Drawing a parallel line using the corresponding-angle test

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What to assume they know

Corresponding angles are equal exactly when the lines are parallel: equal corresponding angles make two lines parallel, and the equality is a two-way test
Perpendicular lines as the case where all four are equal: perpendicular lines, right angles, and the square corner mark
A transversal creates two matching sets of four angles: which line in a three-line figure is the transversal
Handling a set square against a ruler so that neither slips
Folding paper along a straight crease, and folding a crease onto itself

What they should be able to do

Draw two parallel lines using a straight edge and a set square, and name the line that acts as the transversal
State which pair of corresponding angles the construction makes equal, and give their measure
Explain why equality of that one pair is enough to guarantee parallelism
Construct a line through a given point parallel to a given line, using instruments
Do the same construction with two folds, and say what each fold guarantees
State the general result the two constructions share: two lines perpendicular to one line, in the same plane, are parallel to each other
Check a drawn pair of parallels by measuring or tracing corresponding angles, and say why the check is confirmation rather than proof

Where it usually goes wrong

"The set square is what makes the lines parallel." The set square supplies a repeated angle; the corresponding-angle result is what turns a repeated angle into parallelism. Section 5 makes this concrete by repeating a non-right angle and getting parallels anyway.
"Sliding along the ruler is just a way of keeping tidy." It is the step that guarantees the angle is the same angle both times. If the ruler moves, the guarantee is gone and the drawing means nothing.
"I should measure the finished pair to prove it worked." Measuring confirms; the construction proves. The chapter's own note on p.108 already explained why the measurement will be a little off no matter how careful you are.
"The folding method is a different idea from the set-square method." They are the same idea. Both produce two right angles against a common line. Section 10 should show the two figures side by side with the same three lines labelled.
"Any two lines perpendicular to something are parallel." Only if all three lie in one plane. In space, two lines perpendicular to the same line need not be parallel — the same-plane condition from p.110 is doing real work here.
"You can only draw a parallel through a point if the point is conveniently placed." Exactly one parallel passes through any point off the line, and the two-fold method reaches it wherever the point is.

Questions to check understanding

Draw two parallel lines with a set square, and state which angles the method makes equal
Draw the line through a given point parallel to a given line, and describe the method in steps (the printed task at Fig. 5.23, p.119)
Given a folded sheet with two creases at right angles, say which pairs of creases are parallel and why
Explain why checking a single corresponding pair settles the question
Say what would go wrong if the ruler slipped between the two drawings
Given three lines with two right angles marked, state which two are parallel and name the transversal
Fig. 5.34 (p.125) combines a stated perpendicularity with two stated parallelisms, and is the chapter's own examination of this material

Examples worth working on the board

Fig. 5.21 (Part I, §5.7, p.118). Checked against the printed page. A long ruler drawn in green stands nearly upright with the line l ruled along it; a green set square rests against the ruler, and two lines have been drawn along the set square's short edge, out to the right of l. Both new lines carry single-arrow parallel marks. The construction is: rule l; hold the ruler; slide the set square along it; draw once, slide, draw again.
The reason it works (Part I, §5.7, p.118). Inputs: the set square carries a right angle in its own shape, so each new line meets l at 90°; the two new lines are in matching positions on the two sides of l; therefore the corresponding angles are 90° and 90°. Two equal corresponding angles is the condition from §5.6.
Fig. 5.22 (Part I, §5.7, p.118). Checked against the printed page. The same ruler with the set square turned so that its long edge does the drawing; the two lines produced are oblique, not perpendicular to the ruler, and again carry single-arrow parallel marks; the line l is labelled at the lower right. The point of the second grip is that the shared angle no longer has to be 90° — any repeated angle will do. Say that out loud; the printed text does not.
Fig. 5.23 (Part I, Figure it Out, §5.7, p.119). Checked against the printed page. A short horizontal line l with arrowheads at both ends, and a single dot labelled A sitting above and to the right of it. The task is to draw the parallel to l through A with the tools in a geometry box, and then describe the method. The chapter prints no worked solution; the solutions appendix bound after the chapter records a slide-the-set-square method. Do not present that appendix method as the chapter's.
Fig. 5.24 (Part I, p.119). Checked against the printed page. Four panels of a rectangular sheet. Panel 1: a dashed crease l across the sheet. Panel 2: the same, with a dot A marked above l. Panel 3: a second dashed crease t running down through A and meeting l, with a small square marking the right angle. Panel 4: a third dashed crease m through A, across t, and m parallel to l. The only right-angle square in panel 4 is the one at the t–l crossing carried over from panel 3 — verified by the printed page; the book prints no square where m crosses t, even though that fold is a perpendicular too. Inputs: the two folds and their order.
The question that closes the folding passage (Part I, p.120). The page asks why l and m are parallel and leaves it. The answer the chapter has already armed the reader with: t is a transversal to both l and m, and it meets each at 90°, so the two angles in matching positions agree.
The general statement (section 11). Two lines in one plane that are both perpendicular to a third line must themselves be parallel. The chapter demonstrates this twice — once with instruments and once with folds — but never states it as a rule, and it is not in the SUMMARY on p.126. Present it as the generalisation the explanation is drawing, clearly labelled, and note that it needs the same-plane condition from §5.3 exactly as much as the definition did.

Figures to have open

A ruler and a right-angled set square that can be shown sliding, in both the short-edge and long-edge grips, matching Fig. 5.21 and Fig. 5.22. Standard schematic; a photograph is not needed and a redraw is preferable because the angle marks have to stay legible.
A rectangular sheet that can take creases in sequence and unfold between them, matching the four panels of Fig. 5.24. The right-angle mark at the t–l crossing must appear as that fold is made; the printed panels mark no other crossing, so a square drawn where m meets t is an addition made here and should be badged as one.
One diagram that overlays the instrument construction on the folded construction with a common labelling — this figure is the topic's argument and the chapter does not print it.
A line with a marked point off it, for section 8.
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", §5.7 "Drawing Parallel Lines", pp.118–119 — the set-square construction with Fig. 5.21 and Fig. 5.22 (p.118), the Note to the Teacher and the Figure it Out with Fig. 5.23 (p.119)
Same part, the unnumbered block "Making Parallel Lines through Paper Folding", pp.119–120 — the two-fold construction with Fig. 5.24 (p.119) and the closing question (p.120)
Same part, §5.6, pp.117–118, for the corresponding-angle claims the constructions rely on
Same part, §5.2, p.109, for right angles, and §5.3, p.110, for the same-plane condition the general statement needs
Solutions appendix bound after p.126 in the cached PDF (not part of the printed book), for a stepwise method for Fig. 5.23