Question

The diagonals AC and BD of a parallelogram ABCD intersect at O. If P is the mid-point
of AD, prove that
(i) PO || AB (ii) PO =½ CD.
​

Answer 1

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOE

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOEAP=BE (proved above)

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOEAP=BE (proved above)AO=BO (as o is the mid of both the diagonals AC and BD

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOEAP=BE (proved above)AO=BO (as o is the mid of both the diagonals AC and BDAnd,angle O is common

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOEAP=BE (proved above)AO=BO (as o is the mid of both the diagonals AC and BDAnd,angle O is commonTherefore, triangle AOP is congurent to BOE (by SAS congurency rule)

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOEAP=BE (proved above)AO=BO (as o is the mid of both the diagonals AC and BDAnd,angle O is commonTherefore, triangle AOP is congurent to BOE (by SAS congurency rule)Which makes PO=OE(cpct)

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.In triangle AOP and BOEAP=BE (proved above)AO=BO (as o is the mid of both the diagonals AC and BDAnd,angle O is commonTherefore, triangle AOP is congurent to BOE (by SAS congurency rule)Which makes PO=OE(cpct)Therefore PE =AB and AP=BE,which makes them parallel

Answer 2

Answer:

Thank You

Step-by-step explanation:

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