Naming congruent figures so the correspondence is unambiguous

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What to assume they know

SSS: three sidelengths fix a triangle completely — the SSS condition, and the habit of hunting for a side both triangles share
Same shape and same size: superimposition as the test — congruence, and superimposition as its test
Naming a triangle by its three vertices, and knowing that ΔABC and ΔBCA are the same triangle
Tick marks on a diagram as shorthand for "these lengths are equal"
A rectangle has its opposite sides equal

What they should be able to do

Read a congruence statement and say which vertex is claimed to match which
List, from a congruence statement alone and without the figure, which vertices correspond, which sides correspond and which angles correspond
Rewrite a given congruence in every other correct way, and say how many there are
Judge whether a proposed statement expresses the correspondence correctly
Explain what goes wrong when the letters are shuffled on only one side
Use tick marks on a diagram to work out which vertex should pair with which
Find the correspondence in a figure where two triangles overlap or share a side

Where it usually goes wrong

"Once I know they are congruent, any way of writing it will do." The rectangle on pp.7–8 is the counterexample the chapter builds for exactly this. The triangles genuinely are congruent and the proposed statement is still wrong.
"ΔABC ≅ ΔXYZ is the same kind of sentence as AB = XY." The equals sign relates two numbers and does not care which is written first. ≅ relates two ordered triples of vertices. Say this out loud; it is the reason for everything else in the topic.
"You can reorder the letters as long as you keep the same triangle." ΔACB does name the same triangle as ΔABC. That is precisely why the trap works: the picture is unchanged and the claim is not. Only a matched reordering of both names survives.
"The letters are chosen to match, so just read them left to right." In the printed pair on p.6 the second triangle is drawn at a different tilt, and reading the two pictures left to right does not give the right pairing. The tick marks do. Train the eye on the marks.
"A pairing that lists each letter once must be valid." The failed table on p.8 lists each letter exactly once and is still wrong, because it sends a side of one triangle onto a side of the other that has no reason to match it.
"There is one right way to write a congruence." There are six ways to write the same pairing, and the chapter's own exercise on p.8 asks for the other five. Uniqueness is not the point; consistency between the two names is.

Questions to check understanding

Given ΔPQR ≅ ΔSTU, list the corresponding vertices, then the sides, then the angles (the chapter's own instance, and the purest one in the chapter: Figure it Out question 1, Part II, §1.3, p.20, on ΔAIR ≅ ΔFLY)
Given one congruence statement, write out every other correct form of the same claim
Show that one triangle can be congruent to another in more than one way, and say how many distinct correspondences a given pair admits (Figure it Out question 4, Part II, §1.3, p.21)
Decide whether a proposed congruence statement is correctly written, and correct it if not
Given a diagram with tick marks and no letters paired, express the congruence
Given a figure in which two triangles share a side, name the triangles in the order that makes the statement true
Explain, for a stated wrong pairing, which side would land on which
The chapter's own exercises on p.8 and pp.8–9 are of exactly these shapes, and the convention is assumed silently by every later exercise in the chapter

Examples worth working on the board

The two lettered triangles (Part II, §1.2, p.6). Checked against the printed page. On the left, a triangle with C at the top, A at the lower left and B at the lower right. On the right, a second triangle with X at the top, Y at the lower left and Z out to the right; it is drawn in a noticeably different attitude from the first. Tick marks carry the information: one pair of sides is marked with a single stroke, one pair with a double, one pair with a triple, and the marks match across the two triangles. Inputs: the two lettered triangles and their tick marks. The pairing A↔X, B↔Y, C↔Z is what the marks force.
The three lists (Part II, §1.2, pp.6–7). From that one pairing the chapter reads off corresponding vertices, then corresponding sides, then corresponding angles. Three lists, one decision. That is the structure to show.
The annotated congruence (Part II, §1.2, p.7). Checked against the printed page. The statement ΔABC ≅ ΔXYZ is printed twice: once plain, once with the letters coloured and three curved arrows drawn beneath and above it, each arrow running from a letter on the left to the letter in the same position on the right and labelled with the words "corresponds to". Redraw this. It is the best single image in the chapter.
The wrong rewrite and the right one (Part II, §1.2, p.7). Inputs: from ΔABC ≅ ΔXYZ, the chapter marks one rewrite as incorrect — reordering the letters of the first triangle alone — and gives one rewrite that is correct, in which the second and third letters are swapped on both sides at once. That is the rule in miniature: permute both names the same way or not at all.
Fig. 1.1 (Part II, §1.2, p.7). Checked against the printed page. Rectangle ABCD, A top left, B top right, C bottom right, D bottom left, with the segment BD drawn across it. Inputs: AB = CD, AD = CB, and BD belonging to both ΔABD and ΔCDB.
The failed pairing (Part II, §1.2, p.8). Checked against the printed page. The chapter sets out a three-row table pairing A with C, B with B and D with D, then prints a photograph of two pale blue paper triangles cut from a rectangle and laid out to be compared. The verdict is that this pairing lays AB onto CB — two sides with no reason to be equal.
Figure it Out, question 1 (Part II, §1.2, p.8). Input: ΔHEN ≅ ΔBIG. The fixed pairing is H↔B, E↔I, N↔G.
Figure it Out, question 2 (Part II, §1.2, p.8). Checked against the printed page. Two triangles are drawn with side labels only. The first has R at the top left, E at the bottom left and D at the bottom right, with RE = 3.5 cm, ED = 5 cm and DR = 6 cm. The second has J at the left, A at the bottom and M at the top right, with JA = 3.5 cm, AM = 5 cm and MJ = 6 cm.
Figure it Out, question 4 (Part II, §1.2, p.9). Re-checked against p.9. The outline is a dart: D at the apex, F at the lower left, G at the lower right, and E between them but above the F–G level, giving the notched shape D–F–E–G. No segment FG is drawn, and E is not on one. DE runs from apex to notch. Ticks: DF and DG single, FE and GE double. Given: DF = DG and FE = GE, with DE common. The two triangles are congruent by SSS — but the pairing the question writes out is not the one that works, and spotting that is the whole question. This is the exercise this topic exists to prepare.
Figure it Out, question 4 (Part II, §1.3, p.21). Checked against the printed page. Square ABCD with A at the top left, B at the top right, C at the bottom right and D at the bottom left, and the diagonal from A to C drawn. The reader is asked to show that ΔABC ≅ ΔADC, then whether ΔABC is congruent to ΔCDA as well, then — and this middle ask is easy to skip — for further triangle pairs admitting two distinct correspondences, as the square case does; and only after that for a pair admitting six. Inputs: the square and its diagonal. Note: this "six" counts distinct correspondences between one pair of triangles. It is not the six rewrites of a single fixed correspondence that question 1 on p.8 asks for, and merging the two is the easiest mistake this topic can make — see Notes.

Figures to have open

Two congruent triangles in visibly different orientations, lettered, with one, two and three tick marks distinguishing the three pairs of sides. Standard schematic, but the tilt difference matters and must not be tidied away.
The arrow-annotated congruence statement of p.7. Redraw it; it is the topic's central image.
Rectangle ABCD with BD drawn, lettered exactly as Fig. 1.1 letters it.
Two paper-cutout triangles that can be shown sliding over each other, for section 8. Standard schematic — do not lift the book's photograph.
No data table from the textbook is needed.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part II, printed Chapter 1 "Geometric Twins", §1.2 "Congruence of Triangles", unnumbered subheading "Conventions to Express Congruence", pp.6–8 — the two lettered triangles and the three lists (pp.6–7), the annotated ≅ statement and the correct and incorrect rewrites (p.7), Fig. 1.1 and the rectangle argument (pp.7–8), and the failed pairing with its cutout check (p.8)
Same part, same chapter, §1.2, "Figure it Out", questions 1, 2 and 4, pp.8–9
Same part, same chapter, §1.3, "Figure it Out", question 1, p.20 (ΔAIR ≅ ΔFLY) and question 4, p.21 (the square, and the pair congruent in six different ways)
Backward pointer: SSS: three sidelengths fix a triangle completely for the SSS condition this topic applies throughout
Forward pointer: ASA and AAS: two angles are enough to fix the third, where the correspondence has to be read off a crossing rather than off tick marks