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Putnam 1958 B1

Session B

(i) Given line segments $A, B, C, D$ , with $A$ the longest, construct a quadrilateral with these sides and with $A$ and $B$ parallel, when possible. (ii) Given any acute-angled triangle $A B C$ and one altitude $A H$ , select any point $D$ on $A H$ , then draw $B D$ and extend until it intersects $A C$ in $E$ , and draw $C D$ and extend until it intersects $A B$ in $F$ . Prove angle $A H E=$ angle $A H F$ .

Dataset text PutnamGAP. Quoted with source.

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