Two independent ways to classify a triangle: by side and by angle

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What to assume they know

Why a compass beats trial and error for building a triangle — equilateral and isosceles triangles, and comparing sidelengths
Why the three angles of any triangle add to 180° — the angle sum property, which is what makes the definition trap resolvable
What an altitude is, and how to construct one — right-angled triangles, met while constructing altitudes
Comparing an angle with 90°: acute, right, obtuse
Reading tick marks on a figure as a record that two sides are equal

What they should be able to do

Name the three side-based classes and state the condition for each
Read equal-side tick marks off a figure and assign the class
Name the three angle-based classes and state the condition for each
Explain why "acute-angled" has to be defined using all three angles
Show, using the angle sum, that no triangle can have two angles of 90° or more
Assign both a side label and an angle label to a given triangle
State that the relation between the two classifications is left to a later chapter, and avoid assuming it
Explore, by construction, which side-and-angle combinations can occur together

Where it usually goes wrong

"A triangle is either isosceles or right-angled." The two lists are independent; a triangle gets one label from each. A 45°-45°-90° triangle is both, and there is nothing unusual about that.
"Acute-angled means it has an acute angle." Every triangle does, always at least two. The chapter raises this as a Math Talk on p.170 precisely so the student meets the failed definition before the working one.
"A triangle could have two obtuse angles if it were wide enough." Two obtuse angles already total more than 180°. This is the same argument that closed the previous topic's construction question, and it is worth naming as the same argument.
"Scalene means irregular or badly drawn." It is a precise condition: three different sidelengths. Most triangles anyone draws by hand are scalene.
"Equilateral triangles look like they have 60° angles, so that is established." It is not established here. The chapter states plainly on p.170 that the relation between the side classes and the angle classes waits for a later chapter, and it sets the equilateral combinations as construction work for exactly that reason.
"The tick marks are decoration." They are the notation that says which sides are equal. In the three printed figures they are the entire difference between the equilateral and the isosceles picture.
"Right-angled triangles were introduced in this section." They were named in §7.4 on p.169, while constructing altitudes; §7.5 is collecting them, not introducing them.

Questions to check understanding

Given a triangle's three sidelengths, name its side class
Given a triangle's three angles, name its angle class
Give both labels for one triangle, and say which measurements each label used
Explain why a triangle cannot have two right angles, or two obtuse angles
Say why "one acute angle" fails as a definition of an acute-angled triangle
Count how many triangles satisfy a partial specification such as one right angle and one fixed side (the Try This on p.171)
Decide, by construction, whether a stated pair of labels can occur together (the four-part exploration on p.171)
Board-style items ask for a sketch plus a justification, not just the name

Examples worth working on the board

The three side-class figures (Part I, §7.5, p.170). Checked against the printed page. Three triangles drawn side by side and captioned. The first is drawn with a small tick on every one of its three sides. The second carries ticks on two sides only. The third carries no ticks at all. The tick marks are the notation doing the work — they extract as nothing, and an explanation that omits them has removed the only thing distinguishing the first two pictures at a glance.
The angle-class list (Part I, §7.5, p.170). Three names are given and two conditions are stated outright — one right angle, one obtuse angle. The third is set as a Math Talk question first and answered immediately afterwards. Checked against the printed page: no figure accompanies the angle classification. Nowhere on p.170 or p.171 is there a printed picture setting an obtuse-angled triangle beside a right-angled one beside one whose angles are all acute.
The definition trap (Part I, §7.5, p.170). Input: the proposed definition "a triangle with one acute angle", and the instruction to say why it will not do. The reasoning: if two angles were each 90° or more they would already use up the whole 180° and leave nothing for the third, so every triangle has at least two acute angles — which makes "has an acute angle" true of every triangle and therefore useless as a class. The chapter does not print this reasoning; it prints the question and then the corrected definition.
The right-triangle counting problem (Part I, §7.5, p.171). Inputs: ∠B = 90° and AC = 5 cm, with AC taken as base, and the chapter's own hint that the two remaining angles must between them account for 90°.
The four combinations to explore (Part I, §7.5, p.171). Equilateral with a right angle; equilateral with an obtuse angle; isosceles with a right angle; isosceles with an obtuse angle. Note the printed phrasing carefully: the first two are set as things to explore whether they are possible, and the last two are set as things to construct. That asymmetry is a hint.
What the equilateral cases actually need (Part I, §7.5, pp.170–171). To settle the first two by reasoning rather than by drawing, you need to know that equal sides force equal angles — and that link is the very thing §7.5 defers to a later chapter. So the chapter sets the task as construction on purpose. If the explanation gives the answer, it must say which fact it is borrowing and from where; presenting it as a consequence of this chapter is not honest.

Figures to have open

Three triangles differing only in their side pattern, with tick marks that can appear one at a time. Redraw; tick marks must be present, since they are the notation the printed figures rely on.
Three triangles differing in their largest angle, with that angle arced. This trio must be drawn from scratch — the chapter prints no such figure, as confirmed against the printed page p.170 and p.171.
A two-by-three grid of side class against angle class, fillable cell by cell. This is the topic's argument in one image and no printed figure corresponds to it.
An angle sweeping past 90° while the triangle rebuilds, so acute becomes right becomes obtuse in one continuous motion.
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", §7.5 "Types of Triangles", pp.170–171 — the stocktake, the side-based classification with its three figures, the deferral of the relation between the two classifications, the angle-based classification, the Math Talk on defining an acute-angled triangle, and the corrected definition, p.170
Same part, §7.5, p.171 — the Try This on counting right-angled triangles when the side opposite the right angle is fixed, and the four-part construction exploration
Same part, SUMMARY, p.171, seventh and eighth bullets — the chapter's own statement of both classifications
Backward pointers within the same part: §7.1, p.146 and §7.2, p.150, where the side classes were introduced; §7.4, p.169, where right-angled triangles were named; §7.3, p.166, for the angle sum property the definition trap needs