Question

Define Apolloneous Theorem​

Answer 1

Answer:

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that "the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side".

Specifically, in any triangle ABC, if AD is a median, then

{\displaystyle |AB|^{2}+|AC|^{2}=2(|AD|^{2}+|BD|^{2}).}{\displaystyle |AB|^{2}+|AC|^{2}=2(|AD|^{2}+|BD|^{2}).}

It is a special case of Stewart's theorem. For an isosceles triangle with |AB| = |AC|, the median AD is perpendicular to BC and the theorem reduces to the Pythagorean theorem for triangle ADB (or triangle ADC). From the fact that the diagonals of a parallelogram bisect each other, the theorem is equivalent to the parallelogram law.

The theorem is named for the ancient Greek mathematician Apollonius of Perga.

Answer 2

ɢᴇᴏᴍᴇᴛʀʏ, ᴀᴘᴏʟʟᴏɴɪᴜs's ᴛʜᴇᴏʀᴇᴍ ɪs ᴀ ᴛʜᴇᴏʀᴇᴍ ʀᴇʟᴀᴛɪɴɢ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴀ ᴍᴇᴅɪᴀɴ ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴛᴏ ᴛʜᴇ ʟᴇɴɢᴛʜs ᴏғ ɪᴛs sɪᴅᴇs. ɪᴛ sᴛᴀᴛᴇs ᴛʜᴀᴛ "ᴛʜᴇ sᴜᴍ ᴏғ ᴛʜᴇ sϙᴜᴀʀᴇs ᴏғ ᴀɴʏ ᴛᴡᴏ sɪᴅᴇs ᴏғ ᴀɴʏ ᴛʀɪᴀɴɢʟᴇ ᴇϙᴜᴀʟs ᴛᴡɪᴄᴇ ᴛʜᴇ sϙᴜᴀʀᴇ ᴏɴ ʜᴀʟғ ᴛʜᴇ ᴛʜɪʀᴅ sɪᴅᴇ, ᴛᴏɢᴇᴛʜᴇʀ ᴡɪᴛʜ ᴛᴡɪᴄᴇ ᴛʜᴇ sϙᴜᴀʀᴇ ᴏɴ ᴛʜᴇ ᴍᴇᴅɪᴀɴ ʙɪsᴇᴄᴛɪɴɢ ᴛʜᴇ ᴛʜɪʀᴅ sɪᴅᴇ"

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