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# ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).pls explain the fiure.....sure for thumbs up for good answer..

Asked by Saritha , on 19/6/15

In the fig. ABCD is a trapezium with AB II DC.. nd

COnstruction- Draw AC (digonal) . Draw a line XY parallel to AC in which X intersects at AB nd Y intersects at BC

COnsider triangle ADX nd triangle ACX

since these triangles share a common base AX nd lie between same parallels AB nd DC..

Consider triangle ACX nd triangle ACY

since dese triangles share  common base AX and lie between same parallels AC nd XY

ar(ACX)= ar(ACY) --- 2

From 1 and 2

hope u undrstud diss.. if any problem plss tell me!!!

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 17/12/11

hey akshita, from where do u cut nd past all the answers???

Posted by Antra Dshpandy(St Josephs convent girls Sr secondary school) on 17/12/11

hii i did dis ans on my own.. nd its not copied..sorry :)))

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 17/12/11

and can u explain how tro draw this figure accordinf to given information..m confused paaa plsss sure for thumbs up

Posted by Shwetha Boobalanon 17/12/11

m sorry shwetha for lte reply

first draw trapezium abcd.. thn draw the diagonal AC nd then draw XY parallel to AC.. u cn find it wen u do dis X intersects at AB nd Y at BC..

if u didnt still undrstnd plss ask mee..

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 17/12/11

then waht abt DC AND CX.its joined...y..pls answer..

Posted by Shwetha Boobalanon 18/12/11

2)  in a parallelogram , opposite sides are equal..prove this pls..sure for thumbs up 2morrow exam..

Posted by Shwetha Boobalanon 18/12/11

3) if each ppair of opposite sides of a quadrilateral is equal , then its is a prallelogram,

Posted by Shwetha Boobalanon 18/12/11

4) if in a quadrilateral , each pair of opp . angles is equal, then it is a parallelogram..

Posted by Shwetha Boobalanon 18/12/11

5) if the diagonals of a quadrilateria;s bisect each other , then it is II gm ..

id ont know to do the converse of the theorem...can u suggeast me a good idea..plzzzzzzzzz

Posted by Shwetha Boobalanon 18/12/11

ya i got the answer for 5) one could u pls ...do me 2 , 3 , 4 ,plss

Posted by Shwetha Boobalanon 18/12/11

hii shwetha.. DC is a part of trapezium.. nd CX u hve to join in order to prove the triangles r equal

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 18/12/11

2)

In the fig. ABCD is a parallelogram and AC is the diagnol.

To prove - - AB=CD nd AD= BC

Proof

consider triangle ABD nd BCD

1. angle ADB= angle CBD ( alternate interior angle)
2. AC = AC (common)
3. angle ABD= angle CDB ( alternate interior angle)

therefore triangle ADC congruent to triangle ABC (by ASA congruence rule)

ther4 AB= CD (by cpct)

ther4 opp sides of parallelogram r equal

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 18/12/11

3)

In the fig. ABCD is a quadrilateral with diagonal AC.

Given -- AB=CD and AD= BC

To prove - ABCD is a parallelogram, since opp sides r equal, we only hve to prove AB II CD nd AD II BC

Proof

Consider triangle ABD nd triangle BCD

1. AB = CD(given)
3. BD=BD(common)

therefor triangle ABD congruent to triangle BCD (by SSS congruence rule)

angle ABD=CDB(by cpct).. wich implies AB II CD

SInce the opp sides of a quadrilateral r equal nd parallel.. the gvn quadrilateral is a parallelogram..

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 18/12/11

. ...

IN the fig. ABCD is a quadrilateral ...

Given - angle A = angle C ---1

and angle B = angle D --- 2

Adiing equations 1 and 2, 1+2,

we get

angle A + angle B = angle C+ angle D --- 3

We have

angle A + angle B + angle C+ angle D = 360o (angle sum property of a quadrilateral)

FRom 3 v hve, angle A + angle B = angle C+ angle D

therfore

angle A + angle B + angle A + angle B = 360o

2(angle A + angle B) = 360o

angle A + angle B = 360o/ 2

angle A + angle B = 180o  -- 4

angle C  = angle D =180o  ---5

From 4.. AD II BC (since <A nd <B r cointerior angles of the quadrilateral... if the sum of cointerior angles r supplementary thn the sides r parallel to each odr)

Similarly frm 5 AB II CD

Hence ABCD is a parallelogram...

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 18/12/11

this one is liitle bit confusinfg where  did u get the pic...diagram..

Posted by Shwetha Boobalanon 19/12/11

frm net

Posted by Akshita Viswan(GEMS OUR OWN INDIAN SCHOOL) on 19/12/11

hey akshita can u plzz say us d site frm wer u get dese answers plzzz   !!!!!

Posted by Ayasha Affafon 7/2/13

sorry to say this akshita but when u wrote

' 'Consider triangle ACX nd triangle ACY

since dese triangles share common base AX ....... ' '

the base isnt AX it is AC.

Posted by Sakeena Ahmed(SULTAN-UL-ULOOM PUBLIC SCHOOL) on 12/2/13