In figure 1.71, seg XY ∥ seg BC, then which of the following statements is true? (A) AB/AC = AX/AY (B) AX/XB = AY/AC (C) AX/YC = AY/XB (D) AB/YC = AC/XB

Select the appropriate alternative.

In figure 1.71, seg XY ∥ seg BC, then which of the following statements is true?

Figure: \(\triangle ABC\) with X on side AB and Y on side AC.

(A) \(\dfrac{AB}{AC} = \dfrac{AX}{AY}\) (B) \(\dfrac{AX}{XB} = \dfrac{AY}{AC}\) (C) \(\dfrac{AX}{YC} = \dfrac{AY}{XB}\) (D) \(\dfrac{AB}{YC} = \dfrac{AC}{XB}\)

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: (A) \(\dfrac{AB}{AC} = \dfrac{AX}{AY}\)

Since XY ∥ BC, \(\triangle AXY \sim \triangle ABC\) (AA test: \(\angle A\) common, corresponding angles \(\angle AXY \cong \angle ABC\)).

\[\frac{AX}{AB} = \frac{AY}{AC}\]

Rearranging (alternendo), \(\dfrac{AB}{AC} = \dfrac{AX}{AY}\). So (A) is true.

By the basic proportionality theorem the correct form of (B) would be \(\frac{AX}{XB} = \frac{AY}{YC}\), not \(\frac{AY}{AC}\); (C) and (D) mix non-corresponding segments.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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In figure 1.71, seg XY ∥ seg BC, then which of the following statements is true? (A) AB/AC = AX/AY (B) AX/XB = AY/AC (C) AX/YC = AY/XB (D) AB/YC = AC/XB

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