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CBSE Class 10 Answered

in triangle ABC angle A =90 degrees and square DGFE  is inscribed in  it also A-G-B, A-F-C, B-D-E-C AS SHOWN  IN THE FIGURE PROVE THAT SQUARE OF DE=BD * EC
Asked by apurva151 | 07 Dec, 2015, 05:51: PM
answered-by-expert Expert Answer
In space increment BGD angle straight B plus angle BGD equals 90 degree  In space increment ABC angle straight B plus angle straight C equals 90 degree  therefore angle BGD space equals space angle straight C..... left parenthesis 1 right parenthesis  In increment BGD space and space increment FCE angle BGD space equals space angle straight C space space space left square bracket from space left parenthesis 1 right parenthesis right square bracket angle straight D space equals space angle straight E space equals space 90 degree therefore increment BGD space tilde space increment FCE space by space AA space similarity  therefore DB over EF equals DG over EC rightwards double arrow DB cross times EC equals DG cross times EF rightwards double arrow DB cross times EC equals DG cross times DG............... left square bracket sides space of space square right square bracket rightwards double arrow DB cross times EC equals DG squared
Answered by Vijaykumar Wani | 08 Dec, 2015, 12:18: PM
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