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Chapter –10 Practical Geometry In thisChapter, we looked into the methods of some rulerand compasses constructions. Given a line l and a point not on it, we used the idea of ‘equalalternate angles’ in a transversal diagram to drawa line parallel to l. We could also have usedthe idea of‘equal corresponding angles’ to do theconstruction. Construction of Parallel Lines: Draw a linesegment l and mark a pointA not lying on it. Take anypoint B onl and joinB to A. With B as centre and convenient radius, draw an arccutting l at C and ABand D. Now with A as centre and the sameradius as in above stepdraw an arcEF cutting ABat G. Place themetal point of the compasses at C and adjust theopening so that the pencil point is atD. With thesame opening as in above step and withG as centre draw another arccutting the arcEF and H. Now join AHand draw a line m. We studied themethod of drawing a triangle, using indirectly the concept of congruence oftriangles. The following caseswere discussed: (i) SSS: Given thethree side lengths of a triangle. (ii) SAS: Given thelengths of anytwo sides andthe measure ofthe angle between these sides. (iii) ASA: Given themeasures of twoangles and thelength of sideincluded between them. (iv) RHS: Given the length of hypotenuse ofa right-angled triangle and the length of one ofits legs.
Chapter –10 Practical Geometry In thisChapter, we looked into the methods of some rulerand compasses constructions. Given a line l and a point not on it, we used the idea of ‘equalalternate angles’ in a transversal diagram to drawa line parallel to l. We could also have usedthe idea of‘equal corresponding angles’ to do theconstruction. Construction of Parallel Lines: Draw a linesegment l and mark a pointA not lying on it. Take anypoint B onl and joinB to A. With B as centre and convenient radius, draw an arccutting l at C and ABand D. Now with A as centre and the sameradius as in above stepdraw an arcEF cutting ABat G. Place themetal point of the compasses at C and adjust theopening so that the pencil point is atD. With thesame opening as in above step and withG as centre draw another arccutting the arcEF and H. Now join AHand draw a line m. We studied themethod of drawing a triangle, using indirectly the concept of congruence oftriangles. The following caseswere discussed: (i) SSS: Given thethree side lengths of a triangle. (ii) SAS: Given thelengths of anytwo sides andthe measure ofthe angle between these sides. (iii) ASA: Given themeasures of twoangles and thelength of sideincluded between them. (iv) RHS: Given the length of hypotenuse ofa right-angled triangle and the length of one ofits legs.
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