Are the triangles to be proved congruent?
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But it is perfectly possible to draw a diagram meeting all the given facts where ZQ is clearly not the same length as YQ Ė see the diagram I have attached.
Incidentally, notice that the line ZR and the point R are completely irrelevant to this question. This makes me think that there might be some additional fact that you havenít told us about! Could you check to see whether youíve missed something?