Question

The parallel sides of a trapezium are 7cm and 5cm respectively. Find the line segment joining the mid-points of its non-parallel sides.
​

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 it 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]

Answer 2

ɢɪᴠᴇɴ

ɢɪᴠᴇɴᴛʀᴀᴘᴇᴢɪᴜᴍ ᴀʙᴄᴅ

ɢɪᴠᴇɴᴛʀᴀᴘᴇᴢɪᴜᴍ ᴀʙᴄᴅ ᴅɪᴀɢᴏɴᴀʟs ᴀᴄ ᴀɴᴅ ʙᴅ.

ɢɪᴠᴇɴᴛʀᴀᴘᴇᴢɪᴜᴍ ᴀʙᴄᴅ ᴅɪᴀɢᴏɴᴀʟs ᴀᴄ ᴀɴᴅ ʙᴅ. ʟᴇᴛ ᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ᴀᴅ;

ғ ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ʙᴄ.

M ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ᴀᴄ.

N ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ʙᴅ.

ᴇ, ᴍ, ɴ, ᴀɴᴅ ғ ᴀʀᴇ ᴄᴏʟʟɪɴᴇᴀʀ.

ᴜsɪɴɢ ᴀᴅᴄ,

ᴇᴍ ɪs ᴀ ᴍɪᴅsᴇɢᴍᴇɴᴛ,

ᴛʜᴇʀᴇғᴏʀᴇ ɪᴛ ʜᴀs ᴀ ʟᴇɴɢᴛʜ ᴏғ ½ ᴅᴄ = 2.5ᴄᴍ.

ᴜsɪɴɢ ʙᴄᴅ, ɴғ ɪs ᴀ ᴍɪᴅsᴇɢᴍᴇɴᴛ ᴀɴᴅ ʜᴀs ᴀ ʟᴇɴɢᴛʜ ᴏғ ½ ᴅᴄ= 2.5cm .

ᴇғ ɪs ᴀ ᴍɪᴅsᴇɢᴍᴇɴᴛ ᴏғ ᴛʜᴇ ᴛʀᴀᴘᴇᴢɪᴜᴍ, ᴛʜᴇʀᴇғᴏʀᴇ ɪs ʜᴀs ᴀ ʟᴇɴɢᴛʜ ᴏғ

½(DC+AB)= ½(5+7)= 6cm .

6cm .Therefore, MN= 6 − 2 − 2=2cm .