Question 29
Let $M$ be the midpoint of the side $CD$ of the square $ABCD$. The perpendicular from $C$ onto $BM$ meets the lines $BM$ at $N$, and $AB$ at $E$. The line $BM$ intersects the line $AD$ in $P$. Let $F$ be the midpoint of the segment $BN$. Prove that:
a) the triangles $CBE$ and $BAP$ are congruent;
b) the segments $AN$ and $DF$ are congruent and perpendicular.
a) the triangles $CBE$ and $BAP$ are congruent;
b) the segments $AN$ and $DF$ are congruent and perpendicular.