Constructing from two sides and the angle between them

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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

Why a compass beats trial and error for building a triangle — constructing a triangle from three given sidelengths
The triangle inequality: which three lengths can close — that three lengths do not always close, and how to tell
Drawing an angle of a stated size at a given point on a given ray, with a protractor
Class 6 and The four angles at a crossing: vertically opposite and linear pairs: naming an angle by three letters or by its vertex, and reading ∠A off a labelled figure
Marking a point at a measured distance along a drawn ray

What they should be able to do

Identify, in a labelled triangle, which angle is included between two named sides
Read a specimen figure that gives two sidelengths and the angle between them, and say what has been specified
Construct a triangle from two sides and their included angle, in the printed four-step order
Explain why the third side needs no separate check once the first two are drawn
Answer the chapter's open question: whether any such set of measurements can fail, and why
Say what has to go wrong with the given angle before the construction breaks
Distinguish this case from the three-sides case, in terms of what could fail
Predict which parts of the finished triangle were given and which came out of the construction

Where it usually goes wrong

"Any two sides and any one angle will do." The angle has to be the one between the two given sides. Given two sides and an angle somewhere else, the construction is a different problem and this chapter does not take it up.
"Since three lengths can fail, three measurements can always fail." The failure in §7.2 came from three conditions competing for one point. Here the third side is not a condition at all; it is whatever the two arms leave behind. This contrast is the topic's argument and section 8 is where it lands.
"The base has to be the longer of the two given sides." Either given side can be the base. The chapter takes AB = 5 cm because it drew AB first, not because 5 > 4.
"With an obtuse included angle the triangle will not close." It closes; it is simply long and thin. The 120° set on p.161 exists to be built. Note that the chapter draws no obtuse specimen to point at: all three specimen figures on p.160 carry acute included angles, 60°, 30° and 40°, so the obtuse case reaches the student only as a construction task.
"The 45° has to be measured again at the end to check." It cannot have moved. It was drawn, not deduced. The checking habit belongs to the ruler method of §7.1, which this construction replaces.
"A 0° or 180° angle would be a very flat triangle." It would be no triangle — the two arms lie along one line, and all three vertices are collinear. That is the chapter's opening question on p.146 arriving again from a different direction. The chapter does not raise this case, so present it as the explanation probing the boundary of the book's question.

Questions to check understanding

Construct a triangle from two sides and their included angle and list the steps in words (the three sets on p.161 are exactly this task)
Given a labelled triangle and two named sides, name the included angle
State which parts of a finished construction were given and which were derived
Explain why this construction never fails, in terms of what the third side is
Given two sides and an angle that is not between them, say why the method of this section does not directly apply
Given a set of measurements written as length, angle, length, identify what each number is before drawing anything

Examples worth working on the board

The three specimen figures (Part I, §7.3, p.160). Checked against the printed page. Three triangles, each with exactly three of its measurements written on: the first has 3 cm up the left side, 60° at the bottom-left corner and 4 cm along the base; the second has 6 cm along the upper-left side, 30° at the bottom-right corner and 5 cm along the base; the third is a narrow triangle with 2 cm on the left, 40° at the apex and 3 cm on the right. Note that the marked angle is at a different corner in each — the figures are teaching the student to find the included angle, not to look bottom-left every time.
The worked construction (Part I, §7.3, p.160). Inputs: AB = 5 cm as base, ∠A = 45°, AC = 4 cm along the second arm. Two figures accompany it: an in-progress one showing AB with the 45° arm drawn long and unlabelled, and a finished ∆ABC with 4 cm marked on AC, 45° at A and 5 cm on AB.
What came out rather than in (Part I, §7.3, p.160). Three things are given and three are not: BC, ∠B and ∠C are all consequences.
The three sets to construct (Part I, §7.3, p.161). 3 cm, 75°, 7 cm · 6 cm, 25°, 3 cm · 3 cm, 120°, 8 cm. The middle length in each line is the included angle, sitting between the two sidelengths on the page as it sits between them in the figure. The third set is the interesting one: an obtuse included angle, giving a long thin triangle.
The chapter's open question (Part I, §7.3, p.161). It is set as a Math Talk and asks whether any combination of two sides and their included angle fails to produce a triangle, with the justification to come from what the student sees while constructing. The chapter does not print an answer. Checked against every page of the chapter. As long as the given angle is a genuine one — bigger than 0° and smaller than 180° — the two arms genuinely separate, both marked points exist, and joining them always gives a triangle. Say that this is the explanation's answer to the book's question, not the book's own.

Figures to have open

A triangle in which the pair of "given" sides can be re-chosen, so the included angle visibly jumps to a different corner. This is the figure that teaches the word included, and section 2 does not work without it.
A protractor overlay that can be set on a drawn ray to lay off 45°, 120° and 75°. Standard schematic.
A movement of the included angle sweeping continuously from near 0° to near 180°, with the third side redrawn at every stage and collapsing at the two ends. This carries section 10 and is the strongest asset in the topic.
The three specimen figures from p.160, redrawn with the angle mark in a different corner each time.
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", §7.3 "Construction of Triangles When Some Sides and Angles are Given" — the section's opening paragraph, p.160
Same part, within §7.3, the bold unnumbered block "Two Sides and the Included Angle", pp.160–161 — the three specimen figures and the worked ∆ABC with its four steps on p.160; the Figure it Out set and the Math Talk question on p.161
Same part, SUMMARY, p.171, fourth bullet (a) — the chapter's own listing of this as one of the two side-and-angle constructions
Backward pointer: §7.2, pp.151–160, for the contrast with three given sides