IN two triangles ABC and DEF. if AB,AC and AX median are respectivelyproportional to DE,DF and median DY, then prove that trianfle ABC is similar to triangle DEF.

Asked by Amoolya Kamuni | 16th Sep, 2014, 08:43: PM

Expert Answer:

fraction numerator A B over denominator D E end fraction equals fraction numerator A C over denominator D F end fraction equals fraction numerator A X over denominator D Y end fraction left square bracket G i v e n right square bracket I n space increment A B C space a n d space increment D E F comma fraction numerator B X over denominator X C end fraction equals 1 equals fraction numerator E Y over denominator Y F end fraction rightwards double arrow fraction numerator B X over denominator E Y end fraction equals fraction numerator X C over denominator Y F end fraction I n space increment A B X space a n d space increment D E Y comma fraction numerator A B over denominator D E end fraction equals fraction numerator A X over denominator D Y end fraction equals fraction numerator B X over denominator E Y end fraction increment A B X space tilde space increment D E Y space left square bracket S S S right square bracket.... left parenthesis I right parenthesis I n space increment A X C space a n d space increment D Y F comma fraction numerator A C over denominator D F end fraction equals fraction numerator A X over denominator D Y end fraction equals fraction numerator X C over denominator Y F end fraction space increment A X C space tilde space increment D Y F space left square bracket S S S right square bracket...... left parenthesis I I right parenthesis left parenthesis i right parenthesis plus left parenthesis I I right parenthesis increment A B X plus increment A X C space tilde space increment D E Y space plus increment D Y F rightwards double arrow increment A B C space tilde space increment D E F

Answered by Prasenjit Paul | 17th Sep, 2014, 11:21: AM