Answer the 22nd question."DON'T SEND THE SIMILAR QUERY,KINDLY PERFORM THE CORRECT AND STEP BY STEP CALCULATION".
Dear Student,
Please find below the solution to the asked query:
22 ( a ) Given : ABCD is a parallelogram , So
AB | | CD , BC | | AD and AB = CD , BC = AD --- ( 1 )
And ABEF is a parallelogram , So
AB | | EF , BE | | AF and AB = EF , BE = AF --- ( 2 )
i ) From equation 1 and 2 we take : AB | | CD , AB = CD and AB | | EF , AB = EF , So we can say :
CD | | EF ( As AB | | CD and AB | | EF )
And
CD = EF ( As AB = CD and AB = EF )
We know if a pair of sides of any quadrilateral is parallel and equal to each other then that is a parallelogram .
And from above two equations we can say that CDFE is a parallelogram . ( Hence proved )
ii ) As we show CDFE is a parallelogram in previous part and we know in parallelogram opposite sides are equal and parallel to each other , So
FD = EC --- ( 3 ) ( Hence proved )
iii ) In AFD and BEC
AD = BC ( From equation 1 )
AF = BE ( From equation 2 )
And
FD = EC ( From equation 3 )
So,
AFD BEC ( By SSS rule ) ( Hence proved )
22 ( b ) We have our diagram , As :
Here we have join FG and AC
Given : ABCD is a parallelogram So , AB | | CD , BC | | AD and AB = CD , BC = AD --- ( 1 )
And ADEF is a square so , AD = DE = EF = AF and FAD = ADE = DEF = EFA = 90 --- ( 2 )
And AGHB is a square so , AG = GH = HB = AB and AGH = GHB = HBA = BAG = 90 --- ( 3 )
And
FAG = 360 - FAD - BAG - BAD , Substitute values from equation 2 and 3 we get
FAG = 360 - 90 - 90 - BAD ,
FAG = 180 - BAD
We know ABCD is a parallelogram and we know in parallelogram adjacent angles are supplementary .
FAG = ABC --- ( 4 )
In FAG and ABC
AF = BC ( From equation 1 and equation 2 : BC = AD and AD = DE = EF = AF )
AG = AB ( From equation 3 : AG = GH = HB = AB )
And
FAG = ABC ( From equation 4 )
So,
FAG ABC ( By SAS rule )
Then,
FG = AC ( By CPCT ) ( Hence proved )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
22 ( a ) Given : ABCD is a parallelogram , So
AB | | CD , BC | | AD and AB = CD , BC = AD --- ( 1 )
And ABEF is a parallelogram , So
AB | | EF , BE | | AF and AB = EF , BE = AF --- ( 2 )
i ) From equation 1 and 2 we take : AB | | CD , AB = CD and AB | | EF , AB = EF , So we can say :
CD | | EF ( As AB | | CD and AB | | EF )
And
CD = EF ( As AB = CD and AB = EF )
We know if a pair of sides of any quadrilateral is parallel and equal to each other then that is a parallelogram .
And from above two equations we can say that CDFE is a parallelogram . ( Hence proved )
ii ) As we show CDFE is a parallelogram in previous part and we know in parallelogram opposite sides are equal and parallel to each other , So
FD = EC --- ( 3 ) ( Hence proved )
iii ) In AFD and BEC
AD = BC ( From equation 1 )
AF = BE ( From equation 2 )
And
FD = EC ( From equation 3 )
So,
AFD BEC ( By SSS rule ) ( Hence proved )
22 ( b ) We have our diagram , As :
Here we have join FG and AC
Given : ABCD is a parallelogram So , AB | | CD , BC | | AD and AB = CD , BC = AD --- ( 1 )
And ADEF is a square so , AD = DE = EF = AF and FAD = ADE = DEF = EFA = 90 --- ( 2 )
And AGHB is a square so , AG = GH = HB = AB and AGH = GHB = HBA = BAG = 90 --- ( 3 )
And
FAG = 360 - FAD - BAG - BAD , Substitute values from equation 2 and 3 we get
FAG = 360 - 90 - 90 - BAD ,
FAG = 180 - BAD
We know ABCD is a parallelogram and we know in parallelogram adjacent angles are supplementary .
FAG = ABC --- ( 4 )
In FAG and ABC
AF = BC ( From equation 1 and equation 2 : BC = AD and AD = DE = EF = AF )
AG = AB ( From equation 3 : AG = GH = HB = AB )
And
FAG = ABC ( From equation 4 )
So,
FAG ABC ( By SAS rule )
Then,
FG = AC ( By CPCT ) ( Hence proved )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards