ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. -Maths 9th

ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. -Maths 9th
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Since opposite angles are equal in a parallelogram . Therefore , in parallelogram ABCD , we have  ∠A = ∠C  ⇒   1 / 2 ∠A = 1 / 2  ∠C  ⇒ ∠1 = ∠2 ---- i) [∵ AX and CY are bisectors of ∠A  and ∠C respectively] Now, AB | |  DC and the transversal CY intersects them.  ∴ ∠2 and ∠3 ---- ii) [∵  alternate interior angles are equal ] From (i) and (ii) , we have  ∠1 and ∠3 Thus , transversal AB intersects AX and YC at A and Y such that  ∠1 = ∠3 i.e. corresponding angles are equal . ∴ AX | | CY .
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ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. -Maths 9th

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ABCD is a parallelogram and O is the point of intersection of its diagonals. -Maths 9th

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ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. -Maths 9th

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Last Answer : (i) Since diagonals of a parallelogram bisect each other. ∴ O is the mid - point AC as well as BD. In △ADC, OD is a median. ∴ ar(△ADO) = ar(△CDO) [∵ A median of a triangle divide it into two triangles of equal ... and (i) , we have ar(△AOB) - ar(△AOP) = ar(△BOC) - ar(△COP) ⇒ ar(△ABP) = (△CBP)

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