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  1. If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a:
    1. Trapezium
    2. Rectangle
    3. Square
    4. circle
    5. None of these
Correct Option: B

∠AGH = ∠DHG (alt. int. angles)

1∠AGH= 1 ∠DHG= 180
22

Thus, lines GM and HL are intersected by a transversal GH at G and H respectively such that pair of alternate angles are equal, i.e.,
∴ ∠HGM = ∠GHL
∴ GM || HL
Similarly, GL || HM
So, GMHL is a ||gm.
Since AB || CD and EF is a transversal
∴ ∠BGH + ∠DHG = 180° [co-interior angles]
1∠BGH+ 1 ∠DHG= 90°
22

But ∠LGH + ∠LHG + ∠GLH = 180°
∴ 90° + ∠GLH = 180° ⇒ ∠GLH = 90°
Thus, in ||gm GMHL, we have ∠GLH = 90°
Hence, GMHL is a rectangle.



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