Question

prove that if in a triangle the square of one side is equal to the sum of the squares of the other two sides than the angle opposite to the first side is a right angle.​

Answer 1

Answer:

construct a right triangle with altitude and base equal to that of the given triangle

Step-by-step explanation:

Now,

altitude square + base square =hypotenuse

square in a right triangle therefore the triangle we constructed is a right triangle

the altitude an base of the given triangle is equal to that of the constructed triangle.

Applying Pythagoras theorem we get that there hypotenuses shall also be equal.

now applying sss congruency criteria we get that the given and constructed triangles are congruent therefore there corresponding angles shall also be equal applying cpct we can say that the given triangle is a right triangle