Math, asked by adityachoudhary2956, 11 months ago

In Fig. 6.39, ABC and AMP are two right

triangles, right angled at B and M

respectively. Prove that:

(i) Δ ABC ~ Δ AMP

(ii)CA/PA = BC/MP

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Answers

Answered by surendrasahoo

Your answer is in the given attachment

I hope it is helpful....

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Answered by XxMissPaglixX

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ᴀᴀᴀ (ᴀɴɢʟᴇ - ᴀɴɢʟᴇ- ᴀɴɢʟᴇ) sɪᴍɪʟᴀʀɪᴛʏ ᴄʀɪᴛᴇʀɪᴏɴ

ɪɴ ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇs , ɪғ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴀɴɢʟᴇs ᴀʀᴇ ᴇϙᴜᴀʟ , ᴛʜᴇɴ ᴛʜᴇɪʀ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ sɪᴅᴇs ᴀʀᴇ ɪɴ ᴛʜᴇ sᴀᴍᴇ ʀᴀᴛɪᴏ ɪ.ᴇ ᴛʜᴇʏ ᴀʀᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ & ʜᴇɴᴄᴇ ᴛʜᴇ ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ sɪᴍɪʟᴀʀ..

ɪғ ᴛᴡᴏ ᴀɴɢʟᴇs ᴏғ ᴏɴᴇ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ ᴇϙᴜᴀʟ ᴛᴏ ᴛᴡᴏ ᴀɴɢʟᴇs ᴏғ ᴀɴᴏᴛʜᴇʀ ᴛʀɪᴀɴɢʟᴇ ᴛʜᴇɴ ᴛʜᴇ ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ sɪᴍɪʟᴀʀ ʙᴇᴄᴀᴜsᴇ ʙʏ ᴛʜᴇ ᴀɴɢʟᴇ sᴜᴍ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴛʜᴇɪʀ ᴛʜɪʀᴅ ᴀɴɢʟᴇ ᴡɪʟʟ ᴀʟsᴏ ʙᴇ ᴇϙᴜᴀʟ ᴀɴᴅ ɪᴛ ɪs ᴄᴀʟʟᴇᴅ ᴀᴀ sɪᴍɪʟᴀʀɪᴛʏ ᴄʀɪᴛᴇʀɪᴏɴ.

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sᴏʟᴜᴛɪᴏɴ:

ɢɪᴠᴇɴ:

∠ᴀʙᴄ = 90° & ∠ᴀᴍᴘ = 90°

(ɪ) ɪɴ Δᴀʙᴄ ᴀɴᴅ Δᴀᴍᴘ, ᴡᴇ ʜᴀᴠᴇ

∠ᴀ = ∠ᴀ (ᴄᴏᴍᴍᴏɴ ᴀɴɢʟᴇ)

∠ᴀʙᴄ = ∠ᴀᴍᴘ = 90° (ᴇᴀᴄʜ 90°)

∴ Δᴀʙᴄ ~ Δᴀᴍᴘ (ʙʏ ᴀᴀ sɪᴍɪʟᴀʀɪᴛʏ ᴄʀɪᴛᴇʀɪᴏɴ)

(ɪɪ) ᴀs, Δᴀʙᴄ ~ Δᴀᴍᴘ (ʙʏ ᴀᴀ sɪᴍɪʟᴀʀɪᴛʏ ᴄʀɪᴛᴇʀɪᴏɴ)

ɪғ ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ sɪᴍɪʟᴀʀ ᴛʜᴇɴ ᴛʜᴇ ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ sɪᴅᴇs ᴀʀᴇ ᴇϙᴜᴀʟ,

ʜᴇɴᴄᴇ, ᴄᴀ/ᴘᴀ = ʙᴄ/ᴍᴘ

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