In triangles ABC and DEF, addition to the markings, AF = CD and AB || DE. Which of the following methods can NOT be used to prove the triangles congruent?

SSS

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SAS

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AAS

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RHS

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Solution

The correct option is A
SSS

AB || DE. So, $∠ B A C$ = $∠ E D F$ and $∠ B C A$ = $∠ E F D$ (FE || BC, line segments perpendicular to parallel lines are parallel).

Also, it's given that AF = CD

which implies, AF + FC = CD + FC

which is, AC = DF.

So, the triangles can be proven congruent based on SAS, AAS and RHS congruency criteria but not SSS.

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