Question

if the areas of two similar triangles are equal, prove that they are congruent.​

Answer 1

$\huge{\blue{\fcolorbox{blue}{lime}{\boxed{\orange{\bf{\underbrace{\overbrace{\fcolorbox{blue}{black}{\underline{\blue{《 QuEsTiOn》}}}}}}}}}}}$

if the areas of two similar triangles are equal, prove that they are congruent

$\huge \orange{ \overbrace{ \red{\underbrace \color{blue} {\underbrace {\colorbox{blue} {\colorbox{red}{ \color{lime}{\colorbox{black}{ {\red \: {☘answer ☘ }}}}}}}}}}}$

Refer the attachment pls☝️☝️

Answer 2

$\huge\boxed{\fcolorbox{black}{pink}{ꪖꪀร᭙ꫀɾ}}$

⠀⠀⠀⠀⠀

▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀

❑ ɪғ ᴛʜᴇ ᴀʀᴇᴀs ᴏғ ᴛᴡᴏ sɪᴍɪʟᴀʀ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ ᴇǫᴜᴀʟ, ᴘʀᴏᴠᴇ ᴛʜᴀᴛ ᴛʜᴇʏ ᴀʀᴇ ᴄᴏɴɢʀᴜᴇɴᴛ.

⠀⠀⠀⠀⠀

ʟᴇᴛ:- ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇꜱ, △ᴀʙᴄ ᴀɴᴅ △ᴅᴇꜰ

⠀⠀⠀⠀⠀

ɢɪᴠᴇɴ:- ᴀʀᴇᴀ ᴏꜰ ʙᴏᴛʜ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇꜱ ᴀʀᴇ ᴇQᴜᴀʟ ᴀɴᴅ ʙᴏᴛʜ ᴀʀᴇ ꜱɪᴍɪʟᴀʀ

⠀⠀⠀⠀⠀

ᴛᴏ ᴘʀᴏᴠᴇ:- ʙᴏᴛʜ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇꜱ ᴀʀᴇ ᴄᴏɴɢʀᴜᴇɴᴛ, △ᴀʙᴄ ≌ △ᴅᴇꜰ

⠀⠀⠀⠀⠀

ᴘʀᴏᴏꜰ:-

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴀʀᴇᴀ ᴏꜰ ʙᴏᴛʜ ᴛᴇ ᴛʀɪᴀɴɢʟᴇꜱ ᴀʀᴇ ᴇQᴜᴀʟ, ᴛʜᴀᴛ ɪꜱ, ar(△ᴀʙᴄ)= ar(△ᴅᴇꜰ)

$\frac{ar(△ᴀʙᴄ)}{ar(△ᴅᴇꜰ)} = (\frac{ʙᴄ}{ᴇꜰ})^{2} = (\frac{ᴀʙ}{ᴅᴇ})^{2} = (\frac{ᴀᴄ}{ᴅꜰ})^{2}$

$\frac{ar(△ᴅᴇꜰ)}{ar(△ᴅᴇꜰ)} = (\frac{ʙᴄ}{ᴇꜰ})^{2} = (\frac{ᴀʙ}{ᴅᴇ})^{2} = (\frac{ᴀᴄ}{ᴅꜰ})^{2}$

$1 = (\frac{ʙᴄ}{ᴇꜰ})^{2} = (\frac{ᴀʙ}{ᴅᴇ})^{2} = (\frac{ᴀᴄ}{ᴅꜰ})^{2}$

ɴᴏᴡ ᴡᴇ ᴄᴀɴ ᴛᴀᴋᴇ,

$1 = (\frac{ʙᴄ}{ᴇꜰ})^{2}$

$1 = (\frac{ᴀʙ}{ᴅᴇ})^{2}$

$1 = (\frac{ᴀᴄ}{ᴅꜰ})^{2}$

ᴛʜɪꜱ ᴍᴇᴀɴꜱ ᴀʟʟ ᴛʜᴇ ꜱɪᴅᴇꜱ ᴀʀᴇ ᴇQᴜᴀʟ ᴛʜᴀᴛ ɪꜱ,

ʙᴄ=ᴇꜰ

ᴀʙ=ᴅᴇ

ᴀᴄ=ᴅꜰ

ɪɴ △ᴀʙᴄ ᴀɴᴅ △ᴅᴇꜰ

ʙᴄ=ᴇꜰ, ᴀʙ=ᴅᴇ, ᴀᴄ=ᴅꜰ

ᴛʜᴇʀᴇꜰᴏʀᴇ, ʙʏ ꜱꜱꜱ ᴄᴏɴɢʀᴜᴇɴᴄʏ △ᴀʙᴄ ≌ △ᴅᴇꜰ

⠀⠀⠀⠀⠀

ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀

▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅

⠀⠀⠀⠀⠀

$\huge\purple{\mid{\fbox{\tt{ρяєcıσυsтσηє}}\mid}}$