In trapezium $ABGD$, $AB$ is parallel to $DC$ and $E$ and $F$ are the midpoints of the lin

Question

In trapezium $ABGD$, $AB$ is parallel to $DC$ and $E$ and $F$ are the midpoints of the line segments $BD$ and $AC$ respectively. $BFG$ and $DGC$ are straight lines. Prove that $\Delta ABF$ and $\Delta CGF$ are congruent, $EF=\frac{1}{2}(CD-AB)$.

Accepted Answer

(i) Proved: $\triangle ABF\cong\triangle CGF$ (ii) Proved: $EF=\frac12(CD-AB)$

Proofs in Plane Geometry - Midpoint Theorem

Proofs in Plane Geometry - Midpoint Theorem

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