Perpendicular lines as the case where all four are equal

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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
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)

What they should be able to do

State the condition that makes two intersecting lines perpendicular
Derive 90° from "all four angles equal" rather than assuming it
Show that "all four equal" and "one of them is a right angle" are the same condition, using the linear pair
Recognise perpendicular lines when neither of them is horizontal or vertical
Mark perpendicularity on a diagram with the square corner symbol
Name two ways of producing a perpendicular without a protractor — a set square and a paper fold
Explain why perpendicularity is a relation between two lines and not a property of one

Where it usually goes wrong

"Perpendicular means one line across and one line up." Fig. 5.4 is drawn tilted precisely to kill this. Checked against p.109. Nothing about the definition mentions the page's edges.
"You need to measure 90° to make a perpendicular." A set square carries a right angle in its own shape (§5.7, p.118), and a fold that brings a line onto itself produces one with no instrument at all (p.119).
"Perpendicular is something one line is." It is a relation between a pair. Say "perpendicular to", always, and never leave the second line unnamed.
"All four equal is one way to be perpendicular; having a 90° angle is another." They are the same condition, and the linear pair is what makes them the same: if one angle is 90°, its neighbour is 180° − 90° = 90°, and the vertically opposite pair follows. Section 7 should run this both ways.
"90° is just the number someone picked for a right angle." Within this section the number is forced: nothing else divides 180 into two equal parts. The degree itself is a convention; the 90 is not, once the degree is fixed.
"Two perpendicular lines cross at more than the one point." They meet exactly once, like any pair of intersecting lines — the chapter asks this directly on p.107.

Questions to check understanding

Given that two lines cross with all four angles equal, state each angle and justify it
Given one angle of 90° at a crossing, state the other three
Decide from a tilted diagram whether two lines are perpendicular, and say what you checked
Mark the right angles on a gridded figure with the square symbol (this is the printed task in the Figure it Out on p.113)
Describe how to construct a perpendicular to a given line through a given point, using nothing but a set square and a straight edge, or nothing but folds
Read a figure whose givens include a perpendicularity and decide whether the answer actually needs it — Fig. 5.34 (p.125) is exactly this: the perpendicularity is stated and the two required angles do not use it
Say whether "the lines are perpendicular" and "the lines are at right angles" are two facts or one

Examples worth working on the board

The opening question (Part I, §5.2, p.108). The section begins by asking whether a crossing can be drawn with all four angles equal, and then, if so, what each one measures. Both questions are asked before anything is defined. Keep that order.
The derivation (Part I, §5.2, p.109). Inputs: two neighbouring angles at a crossing add to 180°; the four angles are all equal. The chapter states the conclusion — each angle is a right angle, 90° — without writing the one-line equation.
A second, independent check (not in the book). The four angles at a crossing together make a full turn, 360°. Four equal angles therefore give 4x = 360, so x = 90 again. Mark this clearly as an extra route the explanation is supplying: it is not in the chapter, and the chapter's own route runs through the straight angle, not the full turn.
Fig. 5.4 (Part I, p.109). Checked against the printed page. Two lines l and m crossing at right angles, both drawn oblique — neither is horizontal and neither is vertical. The right angle is marked with a small square at the crossing. This is the single most useful thing in the section and it is invisible in the extracted text, because it is entirely a drawing decision. Redraw it, and keep the tilt.
The notation (Part I, "Notations", p.112). Checked against the printed page. Fig. 5.9 shows a set of parallel lines carrying single arrow marks, a second set carrying double arrow marks, and separately a right angle drawn with a small square and labelled 90°.
Two protractor-free constructions. In §5.7, p.118, a set square is slid along a ruler to drop two perpendiculars onto the same line (Fig. 5.21). In the unnumbered folding passage on p.119, a sheet is folded to make a crease perpendicular to a given crease through a chosen point, and then folded again perpendicular to that (Fig. 5.24). Both are previewed here and are worked through in Drawing a parallel line using the corresponding-angle test.
Perpendicularity in the exercises. Fig. 5.11 (p.113) is a square grid carrying shaded polygons — triangles, parallelograms and right trapezia — and asks the reader to mark the right angles with the square symbol and the parallels with arrows. Checked against the printed page. Fig. 5.34 (p.125) states a perpendicularity among its givens — the top line EA stands at right angles to AB — alongside two parallel relations, AB with CD and CD with EF, and one printed angle of 55°. Checked against the printed page, and worked through on the printed page: both of the angles the question asks for follow from the three parallels and that 55° alone, so the perpendicularity is stated but is not what the chase turns on. Worth showing for exactly that reason — a question can hand you more than it needs, and spotting which given did the work is part of reading one.

Figures to have open

A crossing of two lines with all four angles arced equally, mounted so it can be rotated without the angles changing. This is the load-bearing figure of the topic and it must be able to move.
The square corner symbol, drawn large enough to read, matching the mark used in Fig. 5.9 (p.112) and Fig. 5.24 (p.119).
A ruler and a right-angled set square, in the sliding position of Fig. 5.21. Standard schematic; a photograph is not needed.
A rectangular sheet with a crease across it and a second crease perpendicular to the first, for section 10.
No photograph or data table 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", §5.2 "Perpendicular Lines", pp.108–109 — the opening pair of questions (p.108), Fig. 5.4 and the two statements that follow it (p.109)
Same part, §5.1, p.107, for the linear pair the derivation leans on
Same part, the unnumbered block "Notations", p.112, for the square corner mark
Same part, §5.7, p.118, and the unnumbered block "Making Parallel Lines through Paper Folding", p.119, for the two protractor-free constructions
Same part, Figure it Out, p.113 (Fig. 5.11) and p.125 (Fig. 5.34), for where perpendicularity is examined. Fig. 5.34 sits entirely on p.125; the Figure it Out block it belongs to runs pp.123–125.
Same part, SUMMARY, p.126, second bullet