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amitpaswan09
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Asked: 2023-04-01T04:30:15+00:00 In:

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F see figure. Show that F is the mid-point of BC.

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ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F see figure. Show that F is the mid-point of BC.

How are triangles similar by the angle-angle (AA) similarity criterion.
Define the the corresponding sides of similar triangles
NCERT Books for Session 2022-2023 are based on CBSE Board.
Important NCERT Book, Exercise 8.2, Question no: 4, Page No: 150.

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    1. Sir answer hindi me

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    2. Best Answer
      ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F see figure. Show that F is the mid-point of BC.

      In ΔABD,
      E is mid-point of AD [∵ Given]
      and EG ∥ AB [∵ Given]
      Hence, G is mid-point of BD [∵ Converse of Mid-point Theorem]
      Similarly,
      In ΔBCD,
      G is mid-point of BD [∵ Prove above]
      and FG ∥ DC [∵ Given]
      Hence, F is mid-point of BC [∵ Converse of Mid-point Theorem]

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