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., Criteria », , f " AAcriterion :, , “If ZA= and, » ZB=ZQ then, | AABC ~ APQR., , , , , , , , AL\ G theorem, nA J‘, , Similar, Triangles, Area Pythagoras, Similarity Means ‘Same shape theorem, , e.g. All circles are similar., All squares are similar., , , , If AABC ~ APQR: AABC is right angled A (28 = 90°), , AABC ~ ABDC ~ AADB :, fwoaaaee) (By -(A2) -(2e) BC = CD x AC ), Area(APQR) (PQ) (PR) (QR AB’ = CAx AD wii), , Add eq. (i) and (ii), , AB’ + BC’ = CAx AD+CD x AC, , AB’ + BC’ = AC’, , , , , , Some Important Results, 1, The internal bisector of an angle of a triangle divides the opposite side internally in, the ratio of the sides containing the angle., 2. The diagonals of a trapezium divide each other proportionally., , 3. Any line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally, , 4. If three or more parallel lines are intersected by two transversals, then the intercepts, made by them on the transversals are proportional., , 5. In any triangle, the sum of the squares of any two sides is equal to twice the square, of half of the third side together with twice the square of the median which bisects the, third side., , 6. Three times the sum of the squares of the sides of a triangle is equal to four times the, sum of the squares of the medians of the triangle., , , , , , », If As are similar, Then :, A, e ee, Q it ——__ Cc, late US, Pa PR aR 2nd, ZA= 2P, Z2B=2Q, ZE=2R, Basic, Proportionality theorem, (THALES THEOREM), A IF DE| | BC, . then,, AD _AE, B c DB EC, , Converse of B.P.T. :, , eS, DB EC, , DE | | BC., , NCERT / X / Similar Triangles