The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.

Explanation

`Given- D and E " are midpoint of AB and AC"`

`"To prove:" DE"//"BC and DE=1/2BC`

`"construct " CX "//"AB "such that extended DE meet at F"`

`"proof":In /_\ADE and /_\CEF`

`/_A=/_C->"(alternate interior angles)"`

`AED=/_CEF->"(vertically opposite angles)"`

`AE=CE->"(given)"`

`therefore /_\ADE~=/_\CEF-."(angle-side-angle congruency rule )"`

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