Geometric Twins
Class 7 Mathematics · Ganita Prakash Part 2 · Chapter 1
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2- Mathematics
7- Mathematics
- Science
- + 3 more
- 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 congruence — figures that are exact copies of each other, having the same shape and size, so that one can be superimposed exactly on the other (after rotating or flipping if needed). The focus is on congruence of triangles and the minimum measurements needed to guarantee it. You discover four sufficient conditions for general triangles — SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side) and AAS (two angles and a non-included side) — and one special condition for right triangles, RHS (right angle, hypotenuse and one side). Importantly, SSA (two sides and a non-included angle) does not guarantee congruence, since two different triangles can fit those measurements. The correct correspondence of vertices is written carefully, e.g. \(\triangle ABC \cong \triangle XYZ\). Congruence is then used as a tool to prove properties: in an isosceles triangle the angles opposite the equal sides are equal, and every angle of an equilateral triangle is \(60^\circ\).