ABCD is a quadrilateral with midpoints W,X,Y,Z as shown in the diagram below.
Prove that the lines joining the midpoints of the opposite sides bisect each other, giving reasons.
Could anyone please give me a hint on how to start?
ABCD is a quadrilateral with midpoints W,X,Y,Z as shown in the diagram below.
Prove that the lines joining the midpoints of the opposite sides bisect each other, giving reasons.
Could anyone please give me a hint on how to start?
Suppose that $\displaystyle \left\{ E \right\} = \overline {XZ} \cap \overline {WY} $.
By the midpoint theorem $\displaystyle \overline {WX} \parallel \overline {AC} \,\& \,\overline {YZ} \parallel \overline {AC} $.
From that we can get $\displaystyle \Delta XWE \cong \Delta ZYE$.
Now carry on.