&
POSN is trapezium
PQIIN S
Find NS
b
30
S
45
LT = 90°
Answers
Answered by
0
Answer:
Data: In the trapezium ABCD,
AD || BC, AX = XB and DY = YC
To Prove: (i) XY || AD or XY || BC
(ii) XY =
2
1
(AD + BC)
Construction: Extend BA and CD to meet at Z.
Join A and C. Let in cut XY at P
Proof: (i) In △ ZBC, AD || BC [∵ Data]
∴
AB
ZA
=
DC
ZD
[∵ BPT]
∴
2AX
ZA
=
2DY
ZD
[∵ X & Y are mid points of AB and DC]
∴
AX
ZA
=
DY
ZD
⇒XY∣∣AD [∵ Converse of B.P.T.]
(ii) In △ABC, AX = XB [∵ Data]
XP || BC [∵ Proved]
∴ AP = PC [∵ Converse of mid point theorem]
∴ XP =
2
1
BC [∵ Midpoint Theorem]
In △ ADC, PY =
2
1
AD
By adding, we get XP + PY =
2
1
BC +
2
1
AD
∴XY=
2
1
(BC+AD)
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2
Answer:Thanks for free points....
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