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April 5

Vector proof

Given a Quadrilateral $ABCD$ and $E,F$ are midpoints of $AD,BC$ respectively,

Prove: ${\overrightarrow {EF}}={\frac {{\overrightarrow {AB}}+{\overrightarrow {DC}}}{2}}$ . יהודה שמחה ולדמן (talk) 09:44, 5 April 2016 (UTC)[reply]

Please see our note at the top of the page regarding homework. What have you done so far and where are you stuck?

To start you out:

Have you drawn a diagram of the problem?
Do you know and understand why, given the points $W,X,Y,Z$ , then ${\overrightarrow {WZ}}={\overrightarrow {WX}}+{\overrightarrow {XY}}+{\overrightarrow {YZ}}$ ?
How many ways can you represent ${\overrightarrow {EF}}$ in terms of vectors not utilizing the points $E,F$ ?
Can you think of a way to combine those equations so that you can solve for ${\overrightarrow {EF}}$ in the desired terms?