In ∆ 𝐴𝐵𝐶 , if X and Y are the points on AB and AC respectively such that 𝐴𝑋𝑋𝐵 = 34 ,𝐴𝑌 = 5 and 𝑌𝐶 = 9. State whether 𝑋𝑌 || 𝐵𝐶 or not
Question
In ∆ ABC, if X and Y are the points on AB and AC respectively such that:
State whether or not.
Solution
The problem seems to be missing some information. In order to determine whether XY is parallel to BC, we would need to know the ratios of the segments AX:XB and AY:YC. If these ratios are equal, then according to the Converse of the Basic Proportionality Theorem (or Thales' Theorem), XY would be parallel to BC. However, we only know the full lengths of AB and AC, not the individual segments AX, XB, AY, or YC. Therefore, with the given information, we cannot definitively state whether XY is parallel to BC or not.
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