In the figure, ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

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Roy Mcclain · Accepted Answer

Given: ABCD in ||gm, with E as BC&#039;s midpoint. To meet AB produced at F, DE is joined and created.  Proof : In CDE and EBF     &amp;#x2220;   D   E   C   =   &amp;#x2220;   B   E   F      C   E   =   E   B      &amp;#x2220;   D   C   E   =   &amp;#x2220;   E   B   F      &amp;#x2234;   &amp;#x25B3;   C   D   E   &amp;#x2245;   &amp;#x25B3;   B   F   E      &amp;#x2234;   D   C   =   B   F      A   B   =   B   F      A   F   =   A   B   +   B   F   =   A   B   +   A   B      =   2   A   B      A   F   =   2   A   B

In the figure, ABCD is a parallelogram and E is the mid-point of side BC....

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