<prompt> Hlalosa theorem ea Pythagoras.nan  <response>: Instruction in English: Explain the theorem of Pythagoras. . Response in English: The theorem of Pythagoras, also known as Pythagorean Theorem, is one of the most fundamental concepts in mathematics, particularly in geometry. It was named after the ancient Greek mathematician Pythagoras, who is widely credited with its discovery although it may have been known to the Indians and the Babylonians prior to him.The theorem relates to the three sides of a right-angled triangle, which is a triangle with one angle equal to 90 degrees. Simply put, the theorem states that in a right angled triangle, the square of the length of the hypotenuse the side opposite to the right angle is equal to the sum of the squares of the length of the other two sides. This relationship can be expressed algebraically as: c2 a2 b2 where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.For example, consider a right angled triangle with sides 3 and 4 units long. According to Pythagorean theorem, the length of the hypotenuse would be given as: c2 32 42 9 16 25, giving c 5. The theorem has numerous applications in mathematics, physics, and engineering- any time one needs to determine the relations between sides of right-angled triangles, and despite its ancient origins, is an invaluable tool for problem-solving today. . Response in Sesotho: Khopolo ea Pythagoras, eo hape e tsejoang ka hore ke Pythagorean Theorem, ke e ngoe ea mehopolo ea mantlha ea lipalo, haholo ho jeometry. E rehelletsoe ka setsebi sa lipalo sa Mogerike sa boholo-holo Pythagoras, eo ho lumeloang hore ke sona se sibolotseng le hoja e ka na eaba se ne se tsejoa ke Maindia le Bababylona pele ho eena. Theorem e amana le mahlakore a mararo a kgutlotharo e nang le kgutlotharo e nepahetseng, e leng kgutlotharo e nang le kgutlotharo e le nngwe e lekanang le dikgato tse 90. Ka mantsoe a bonolo feela, theorem e bolela hore ka khutlotharo e nepahetseng ea angled, sekoere sa bolelele ba hypotenuse lehlakore le le leng le shebaneng le lehlakoreng le letona le lekana le kakaretso ea lisekoere tsa bolelele ba mahlakore a mang a mabeli. Kamano ena e ka hlalosoa ka aljebra ka hore: c2 a2 b2 moo c e leng bolelele ba hypotenuse, le a le b e le bolelele ba mahlakore a mang a mabeli. Mohlala, nahana ka kgutlotharo e nang le mahlakore a 3 le diyuniti tse 4 ka bolelele. Ho ea ka khopolo ea Pythagorean, bolelele ba hypotenuse bo ne bo tla fanoa e le: c2 32 42 9 16 25, ho fana ka c 5. Theorem e na le litšebeliso tse ngata ho lipalo, fisiks le boenjiniere. - nako efe kapa efe ha motho a hloka ho tseba likamano lipakeng tsa mahlakore a likhutlo li tharo tse ka letsohong le letona, me ho sa tsotelehe tšimoloho ea eona ea khale, ke sesebelisoa sa bohlokoa sa ho rarolla mathata kajeno. 