Question

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∆ABC is a right triangle, right angled at A and AD parallel to BC, then, AD is equal to


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Answer 1

Step-by-step explanation:

_______________-------___

Answer 2

ɢɪᴠᴇɴ Δᴀʙᴄ ɪs ᴀ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ ʀɪɢʜᴛ-ᴀɴɢʟᴇᴅ ᴀᴛ ᴀ ᴀɴᴅ ᴀᴅ ⊥ ʙᴄ. ⇒ ∠ᴄᴀᴅ + ∠ʙᴀᴅ = ° …

() ⇒ ∠ʙᴀᴅ + ∠ᴀʙᴅ = ° …

() ғʀᴏᴍ () ᴀɴᴅ (),

∠ᴄᴀᴅ = ∠ᴀʙᴅ ʙʏ ᴀᴀ sɪᴍɪʟᴀʀɪᴛʏ, ɪɴ Δᴀᴅʙ ᴀɴᴅ Δᴀᴅᴄ,

⇒ ∠ᴀᴅʙ = ∠ᴀᴅᴄ [° ᴇᴀᴄʜ]

⇒ ∠ᴀʙᴅ = ∠ᴄᴀᴅ ∴ Δᴀᴅʙ ~ Δᴀᴅᴄ

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ɪғ ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ sɪᴍɪʟᴀʀ, ᴛʜᴇɪʀ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴀɴɢʟᴇs ᴀʀᴇ ᴇǫᴜᴀʟ ᴀɴᴅ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ sɪᴅᴇs ᴀʀᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ. ʟᴀsᴛ ʟɪɴᴇ ᴀ

ᴅ ᴄ ᴅ = ᴀ ʙ ᴀ ᴄ = ʙ ᴅ ᴀ ᴅ . . .

( ) ᴀᴅᴄᴅ=ᴀʙᴀᴄ=ʙᴅᴀᴅ...

() ᴛʜᴇʀᴇғᴏʀᴇ,

ᴀ ᴅ ᴄ ᴅ = ʙ ᴅ ᴀ ᴅ ᴀᴅᴄᴅ=ʙᴅᴀᴅ

⇒ ʙ ᴅ = ᴀ ᴅ ᴄ ᴅ

⇒ʙᴅ=ᴀᴅᴄᴅ

⇒ ʙ ᴅ ᴄ ᴅ = ᴀ ᴅ ᴄ ᴅ = ( ᴀ ᴅ ᴄ ᴅ )

⇒ʙᴅᴄᴅ=ᴀᴅᴄᴅ=(ᴀᴅᴄᴅ) = ( ᴀ ʙ ᴀ ᴄ ) =(ᴀʙᴀᴄ) ( ∵ ᴀ ᴅ ᴄ ᴅ = ᴀ ʙ ᴀ ᴄ (∵ᴀᴅᴄᴅ=ᴀʙᴀᴄ ғʀᴏᴍ ())

ʜᴇɴᴄᴇ, ʙ ᴅ ᴅ ᴄ = ( ᴀ ʙ ᴀ ᴄ ) ʙᴅᴅᴄ=(ᴀʙᴀᴄ)

ᴏᴘᴛɪᴏɴ (ᴀ) ɪs ᴄᴏʀʀᴇᴄᴛ.