Question

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Answer 1

Answer:

in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]

Pythagorean theorem

The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

{\displaystyle a^{2}+b^{2}=c^{2},}a^{2}+b^{2}=c^{2},

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. The theorem, whose history is the subject of much debate, is named for the Greek thinker Pythagoras, born around 570 BC.

Answer 2

$\huge\red{\underline{{\bf ᴀ}}}\huge\green{\underline{{\bf ɴ}}}\huge\red{\underline{{\bf s}}}\huge\green{\underline{{\bf ᴡ}}}\huge\red{\underline{{\bf ᴇ}}}\huge\green{\underline{{\bf ʀ}}}$

Dᴇғɪɴɪᴛɪᴏɴ:-

• Pʏᴛʜᴏɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪɴ ᴀ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇ, ᴛʜᴇ sqᴜᴀʀᴇ ᴏғ Hʏᴘᴏᴛᴇɴᴜsᴇ ɪs ᴇqᴜᴀʟ ᴛᴏ ᴛʜᴇ sᴜᴍ ᴏғ sqᴜᴀʀᴇs ᴏғ ɪᴛs Bᴀsᴇ ᴀɴᴅ Hᴇɪɢʜᴛ.

Cᴏɴᴠᴇʀsᴇ ᴏғ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ:-

• Tʜɪs ɪs ᴊᴜsᴛ ᴛʜᴇ ᴄᴏɴᴠᴇʀsᴇ ᴀɴᴅ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏғ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ. Iᴛ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪғ ᴛʜᴇ sqᴜᴀʀᴇ ᴏғ Hʏᴘᴏᴛᴇɴᴜsᴇ ɪs ᴇqᴜᴀʟ ᴛᴏ ᴛʜᴇ sᴜᴍ ᴏғ sqᴜᴀʀᴇs ᴏғ ɪᴛs Bᴀsᴇ ᴀɴᴅ Hᴇɪɢʜᴛ, ᴛʜᴇɴᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ɪs Rɪɢʜᴛ Aɴɢʟᴇᴅ Tʀɪᴀɴɢʟᴇ.

Tʜɪs ᴛʜᴇᴏʀᴇᴍ ᴄᴀɴ ʙᴇ ғᴏʀᴍᴜʟᴀᴛᴇᴅ ᴀs,

$\;\large{\boxed{\bf{\red{(Hypotenuse)^{2}\;=\;(Base)^{2}\;+\;(Height)^{2}}}}}$

$\;\bf{\green{\rightarrow\;\;(Hypotenuse)^{2}\;-\;(Base)^{2}\;=\;(Height)^{2}}}$

$\;\bf{\red{\rightarrow\;\;(Hypotenuse)^{2}\;-\;(Height)^{2}\;=\;(Base)^{2}}}$