A Tale of Three Intersecting Lines
Class 7 Mathematics · Ganita Prakash Part 1 · Chapter 7
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7- Mathematics
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- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Social Science
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Summary
This chapter is about triangles — their construction, existence and angle properties. Using a compass and ruler you construct equilateral triangles (all sides equal), isosceles triangles (two sides equal) and scalene triangles (all sides different) by drawing arcs from the endpoints of a base. A central idea is the triangle inequality: a triangle exists only when each side is shorter than the sum of the other two. So lengths like 10, 15, 30 cannot form a triangle because \(30 > 10 + 15\), whereas 4, 5, 8 can because \(8 < 4 + 5\). You also construct triangles from two sides and the included angle, or two angles and the included side, and discover that a triangle needs the two given angles to sum to less than \(180^\circ\). By drawing a line parallel to the base through the top vertex, you prove the angle sum property: the three angles of any triangle add to \(180^\circ\). You meet exterior angles, altitudes (perpendiculars from a vertex to the opposite side), and classify triangles by sides and by angles (acute, right, obtuse).