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Similarity and Congruence
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
Two figures are congruent if one can be placed exactly on the other by sliding, turning or flipping. Every matching side and angle is equal. You only need three matching facts (one of the rules) to be sure.
SSS: three sides match. SAS: two sides and the angle between them. ASA (or AAS): two angles and a corresponding side. RHS: right angle, hypotenuse and one side - for right triangles only.
Similar figures have equal angles and sides in the same ratio. The ratio is the scale factor k. AA (two equal angles) is the easiest test for triangles.
If lengths scale by k, areas scale by k² and volumes by k³. Double the length and the area is four times bigger, the volume eight times.
Hard words & meanings
| congruent | having exactly the same shape and size; symbol ≅ |
| similar | having the same shape with all sides in the same ratio; symbol ~ |
| scale factor | the number k that every length is multiplied by, equal to new length over old length |
| corresponding | matching parts that occupy the same position in two figures |
| included angle | the angle formed between two named sides of a triangle |
| hypotenuse | the longest side of a right-angled triangle, opposite the right angle |
| ratio | a comparison of two quantities by division, written a:b |
| Basic Proportionality Theorem | a line parallel to one side of a triangle divides the other two sides in the same ratio (Thales' theorem) |
Model exam answers, grammar & audio
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