In the given figure, seg XY || seg BC, then which of the following statements is true?
Problem Set 1 | Q 1.5 | Page 26
In the given figure, seg XY || seg BC, then which of the following statements is true?
AB/AC = AX/AY
AX/XB =AY/AC
AX/YC = AY/XB
AB/YC = AC/XB
Solution
Given: seg XY || seg BC
AX/BX = AY/YC .......(By basic proportionality theorem)
∆ABC and ∆DEF are equilateral triangles. ...(Given)
⇒ (BX/AX) + 1 = (YC/AY) + 1
⇒ (BX + AX)/AX = (YC + AY)/AY
⇒ AB/AX = AC/AY
⇒ AB/AC = AX/AY
Hence, the correct option is AB/AC = AX/AY
Answer:- In the given figure, since seg XY || seg BC, we have:
∆ABX ~ ∆YAC (by AA similarity)
Therefore, we have:
AB/AC = AX/AY
So, option (a) is the correct answer.
Problem Set 1 | Q 1.5 | Page 26
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