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Maths · The slope of a line, parallel and perpendicular lines

Assertion If in a a line intersects in and in then Reason If a line is drawn par

Assertion If in a \( \triangle A B C, \) a line \( D E \| B C \) intersects \( A B \) in \( D \) and \( A C \) in \( E, \) then \( \frac{A B}{A D}=\frac{A C}{A E} \) Reason If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

  • A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
  • C. Assertion is correct but Reason is incorrect
  • D. Assertion is incorrect but Reason is correct

Step-by-step solution

Assertion: In triangle ABC, DE parallel to BC implies that triangles ADE and ABC are similar (by AA similarity). Hence, corresponding sides are proportional: AD/AB = AE/AC. Inverting gives AB/AD = AC/AE. Reason: This is the Basic Proportionality Theorem (Thales' theorem), which states that a line parallel to one side divides the other two sides proportionally. Thus, both are correct and Reason correctly explains Assertion.
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