Math, asked by sksahoo1278, 10 months ago

D,E,F are the midpoint of BC,CA And AB respectively .prove that AD insects EF

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Answered by ppbarchanabhatt

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Answered by Anonymous

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☺✌◦•●◉✿ ɢɪᴠᴇɴ

ᴀʙᴄ ɪs ᴀ ᴛʀɪᴀɴɢʟᴇ.

ᴘ ɪs ᴛʜᴇ ᴍ.ᴘ ᴏғ ʙᴄ

ϙ ɪs ᴛʜᴇ ᴍ.ᴘ ᴏғ ᴄᴀ

ʀ ɪs ᴛʜᴇ ᴍ.ᴘ ᴏғ ᴀʙ

ᴛᴏ ᴘʀᴏᴠᴇ

xʏ = ʙᴄ

ᴘʀᴏᴏғ

ɪɴ Δᴀʙᴄ

ʀ ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ᴀʙ.

ϙ ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ᴀᴄ.

∴ ʙʏ ᴍɪᴅᴘᴏɪɴᴛ ᴛʜᴇᴏʀᴇᴍ,

ʀϙ║ʙᴄ

ʀϙ║ʙᴘ → 1 [ᴘᴀʀᴛs ᴏғ ᴘᴀʀᴀʟʟᴇʟ ʟɪɴᴇs]

ʀϙ = ʙᴄ → 2

sɪɴᴄᴇ ᴘ ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ʙᴄ,

ʀϙ = ʙᴘ → 3

ғʀᴏᴍ 1 ᴀɴᴅ 3,

ʙᴘϙʀ ɪs ᴀ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ.

ʙϙ ᴀɴᴅ ᴘʀ ɪɴᴛᴇʀsᴇᴄᴛ ᴀᴛ x

sɪᴍɪʟᴀʀʟʏ,

ᴘᴄϙʀ ɪs ᴀ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ.

ᴘϙ ᴀɴᴅ ᴄʀ ɪɴᴛᴇʀsᴇᴄᴛ ᴀᴛ ʏ.

x ᴀɴᴅ ʏ ᴀʀᴇ ᴍɪᴅᴘᴏɪɴᴛs ᴏғ sɪᴅᴇs ᴘʀ ᴀɴᴅ ᴘϙ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.

ɪɴ Δᴘϙʀ

x ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ᴘʀ

ʏ ɪs ᴛʜᴇ ᴍɪᴅᴘᴏɪɴᴛ ᴏғ ᴘϙ

∴ ʙʏ ᴍɪᴅᴘᴏɪɴᴛ ᴛʜᴇᴏʀᴇᴍ,

xʏ = ʀϙ

ғʀᴏᴍ 3,

xʏ = + ʙᴄ

xʏ = ʙᴄ

ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ.☺✌

✿◉●•◦

. Bhai mark kar de naa Brainliest....!

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