The Encyclopedia of Geometry (0029)


Problem

Two triangles, in which a pair of corresponding sides and angles at both ends of them are respectively equal, are congruent.


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Solution

Now, if we put $B$ on top of E, $C$ on top of $F$, and $A$ on the same side of $EF$ as $D$, then

$$∠B=∠E.$$

Thus, $BA$ overlaps $ED$.

Since $∠C=∠F$, $CA$ overlaps $FD$.

Therefore, $A$ overlaps $D$.

$$∴ \ △ABC≡△DEF.$$

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Reference

Teiichiro Sasabe (1976) The Encyclopedia of Geometry (2nd edition), Seikyo-Shinsha, p.9