Class 7 Maths Ch 7: Two independent ways to classify a triangle: by side and by angle

Sorting triangles by sides and sorting them by angles are not two halves of one list. They are two separate questions put to the same shape. Full topic page, with the transcript and the exact book reference: https://prepshorts.com/learn/class-7/... Sorting triangles by their sides and sorting them by their angles are not two halves of one list. They are two separate questions put to the same triangle, and every triangle answers both - it comes away with one label from each, which is why a triangle is never just one kind of thing. The first question looks at lengths and nothing else: three the same is equilateral, two the same isosceles, none the same scalene, and there is no fourth answer. On paper a drawing is never accurate enough to be trusted, so a small stroke across a side declares it equal to any side carrying the same stroke - take the strokes away and the equilateral and the isosceles picture are the same picture. Scalene is not the leftover bin: of every triangle you can build with whole-number sides up to 60 cm - 19,375 of them - 60 are equilateral, 2,640 have exactly two sides equal and the remaining 16,675, 86 per cent, are scalene. Whether an equilateral triangle also counts as isosceles is left open here on purpose; the condition says two equal sides and does not say exactly two, and the two readings differ by exactly those 60 shapes. The second question ignores the sides. One right angle makes it right-angled; one obtuse angle makes it obtuse-angled, and only ever one, because the smallest pair of obtuse angles is 91 and 91 and that is 182 before the third corner is paid for. Then the trap the video gives a whole chapter to: "acute-angled" cannot mean "has an acute angle". CHAPTERS 0:00 Two questions, not one list 0:47 Sorting by sides 1:26 The tick marks 2:15 Scalene is the ordinary case 3:39 Sorting by angles 4:36 The definition that sorts nothing 5:18 Why every triangle has two 6:05 Acute-angled means all three 6:50 One angle, opening 7:42 Two labels at once 8:39 The two empty boxes 9:42 How many is endlessly many IN THE BOOK Class 7 Mathematics, Chapter 7, "A Tale of Three Intersecting Lines". NCERT Ganita Prakash — Textbook of Mathematics for Grade 7 (NCF-SE 2023), Part I, First Edition April 2025. ABOUT PREPSHORTS One short video per NCERT topic, with the book open beside it. Not worked answers to the exercises — the reason each result has to hold, which is the half that carries into a question you have not seen before. The full library is 708 videos across Classes 6 to 12, about 147 hours in all. 88 are free to watch, one opening every chapter. https://prepshorts.com/?utm_source=yo...