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PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. then
  • a)
    PS ≠ PT
  • b)
    PS < PT
  • c)
    PS = PT
  • d)
    PS > PT
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
PQR is a triangle in which PQ = PR and S is any point on the side PQ. ...
Since ST is parallel to QR and S is on PQ, by the Basic Proportionality Theorem (or Thales' theorem):
PS/SQ = PT/TR
However, since PQ=PR, triangles △PSQ and △PRT are similar due to the AA (Angle-Angle) criterion (one angle is common, and the other angles are corresponding angles formed by the parallel lines).
PS/SQ = PT/TR = 1
PS = PT
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Most Upvoted Answer
PQR is a triangle in which PQ = PR and S is any point on the side PQ. ...
Option C is correct here
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