we know that
The [tex]45\°-90\°-45\°[/tex] triangle of the figure is an isosceles right triangle
so
The triangle has two equal sides and two equal angles
The two equal sides are called legs
The third side is called hypotenuse
Let
a,b-----> the legs of the triangle
c------> the hypotenuse
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
so
[tex]a=b[/tex]
[tex]c> a[/tex] -------> [tex]a<c[/tex]
[tex]c> b[/tex] -------> [tex]b<c[/tex]
Two sides have the same length, which is less than the length of the third side
Statements
case A) Each side has a different length
The statement is False
Because, two length sides are equal
case B) Two sides have the same length, which is less than the length of the third side
The statement is True
See the procedure
case C) The three sides have the same length
The statement is False
Because, two length sides are equal and the third lenght side is different
case D) The sum of the lengths of two sides is equal to the length of the third side
The statement is False
Because, the sum of the squares of the legs equals the square of the hypotenuse
therefore
the answer is
Two sides have the same length, which is less than the length of the third side
