What an altitude is, and how to construct one

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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

Perpendicular lines, and the right-angle mark on a figure
Perpendicular lines as the case where all four are equal and Chapter 5 (Part I): perpendicular lines and how to produce one without a protractor, and the words perpendicular and line segment
Why a compass beats trial and error for building a triangle — vertices, sides, and choosing a base
Handling a set square and a ruler together
The idea that a length is measured along a segment with two named endpoints

What they should be able to do

State what makes a segment an altitude of a triangle
Identify, in a labelled figure, which vertex an altitude comes from and which side it lands on
Explain why every triangle has three altitudes, and why they are generally of different lengths
Say what "the height of the triangle" means and why the phrase is incomplete without a base
Construct the altitude from a vertex to a base using a set square and a ruler
Construct an altitude in an obtuse triangle, extending the base first
Justify why a paper fold that brings the base onto itself produces a perpendicular crease
Recognise the one kind of triangle where a side doubles as an altitude, and name that kind

Where it usually goes wrong

"The altitude is the line from the top corner straight down the page." Down the page is only vertical if the base happens to be horizontal. What is required is a right angle with the base, whatever direction that base runs in.
"A triangle has one height." It has three, one per vertex, and they are generally all different. The phrase "the height of the triangle" is shorthand for the one belonging to the base currently in use, and the chapter says so.
"The altitude bisects the base" or "the altitude bisects the angle it comes from." Neither is true in general. Fig. 7.8 is drawn lopsided precisely so that D is not the midpoint of BC. Neither median nor bisector is printed anywhere in this chapter.
"An altitude has to lie inside the triangle." In an obtuse triangle two of the three altitudes fall outside, and the chapter shows one of them. The definition never mentioned inside.
"If the foot is outside, the base has grown longer." The extension is a drawing aid, not part of the triangle. BC still measures what it measured; the line through B and C is what got longer.
"Freehand is close enough." The chapter explicitly rejects ruler-only accuracy for this and brings in a set square. The point is that a right angle drawn by eye is the one thing this construction cannot afford to approximate.
"The three altitudes meet at a point, so that point must matter here." The chapter neither states nor names any such point, and its figure on p.168 draws only two of the three altitudes. Do not import a concurrency claim into the explanation.

Questions to check understanding

Construct a triangle to given measurements and then construct a named altitude (both printed items on p.170 are exactly this, and the 140° one is the graded version)
Given a labelled figure, name the base each drawn altitude belongs to
Explain why an altitude may fall outside the triangle, and when
Justify why a fold that brings one half of the base onto the other gives a perpendicular crease
Identify which side of a right triangle is also an altitude, and to what
Say why a set square is used instead of a ruler alone
Given a triangle drawn on an unusual slant, construct the altitude to a non-horizontal base — this is where the "straight down the page" error shows up

Examples worth working on the board

Fig. 7.8 (Part I, §7.4, p.167). Checked against the printed page. A triangle with B at the lower left, C at the lower right and A above and to the right; the perpendicular from A meets BC at D, which sits between B and C but distinctly nearer C, and the right angle at D is marked with a square. Note that this is a scalene, visibly lopsided triangle — the altitude is not down the middle of anything.
The three-altitude figure (Part I, §7.4, p.168). Checked against the printed page. A triangle with A at the top right, B at the lower left, C at the lower right. F is marked on AB, E on AC, each with a right-angle square, and the segments from C to F and from B to E are drawn and cross inside the triangle. AD is not drawn in this second figure — it was the subject of Fig. 7.8.
The obtuse pair (Part I, §7.4, p.168). Checked against the printed page. Two versions of the same triangle side by side. In the first, A is at the upper left, B below it and C to the lower right, and there is nowhere on BC directly beneath A. In the second, the base line has been extended to the left past B to a new point D, and AD is drawn as a dashed segment. Inputs: the triangle and the instruction to extend.
The paper fold (Part I, §7.4, p.168). Inputs: a paper triangle, a chosen base, and a fold that brings the top vertex down so the crease runs to the base. The justification asked for is why the crease must meet the base at a right angle — a fold that lays one half of the base onto the other makes two equal angles along a straight line, and two equal angles totalling 180° are 90° each. That reasoning is added here; the chapter sets it as a task.
The set square method (Part I, §7.4, pp.168–169). Checked against the printed page. Three steps, each with a figure. In Step 1 the ruler lies along the base with the set square standing on it, one leg of its right angle flat against the ruler and the set square to the left of the triangle. In Step 2 the set square has been slid right until its upright edge touches A. In Step 3 the altitude is drawn along that upright edge. Inputs: the tools and the three moves.
The right triangle (Part I, §7.4, p.169). Checked against the printed page. A triangle with the right angle at B, marked with a square; A above B and C to the right, so AB is vertical and BC horizontal. — together with the figure, and let it identify which side does the job and against which base.
The two constructions set as practice (Part I, §7.5, p.170). The first is an isosceles ∆ABC: base BC of 5 cm, side CA also 5 cm, side AB 6 cm; then drop the altitude from A. The second is ∆TRY, where a 140° angle at R sits between a 7 cm arm TR and a 4 cm arm RY; then drop the altitude from T. The second is the one that matters — with 140° at R the foot lands off the end of RY, so the base line has to be extended first. Note the printed position: both items sit under the §7.5 heading on p.170 even though they are §7.4 work.

Figures to have open

A triangle that can be rotated so each of its three sides becomes the base in turn, with the corresponding altitude redrawn each time. Sections 4 and 5 both depend on this and it is the topic's central asset.
An obtuse triangle whose base line can be extended, with the altitude shown dashed outside the figure, matching the p.168 pair.
A set square and ruler that can be shown sliding along each other. Standard schematic; the sliding is the whole method.
A paper triangle foldable, with the two angles either side of the crease marked equal.
A right triangle with the right angle marked, where one side can be highlighted as doubling for an altitude.
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 7 "A Tale of Three Intersecting Lines", §7.4 "Constructions Related to Altitudes of Triangles", pp.167–169 — the everyday-heights opening and Fig. 7.8 with the definition, p.167; the three-altitude figure, the note on what "height of the triangle" means, and the obtuse pair, p.168
Same part, within §7.4, the bold unnumbered blocks "Altitudes Using Paper Folding" and "Construction of the Altitudes of a Triangle", pp.168–169 — the folding task, the case for the set square, and the three construction steps; the right triangle and its naming, p.169
Same part, §7.5 "Types of Triangles", p.170, Figure it Out items 1 and 2 — two altitude constructions printed under the next section's heading
Same part, SUMMARY, p.171, sixth bullet — the chapter's own one-line definition of an altitude
Backward pointer: Part I, printed Chapter 5 "Parallel and Intersecting Lines", for perpendiculars and for constructing them