Question

&
POSN is trapezium
PQIIN S
Find NS
b
30
S
45
LT = 90°​

Answer 1

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)

Answer 2

Answer:Thanks for free points....