Question

Raj made this argument:

The Triangle Inequality Theorem states that if the lengths of three sides of a triangle are a, b, and c, then a + b > c. For this reason, since a, b, and c are all positive numbers, the square of a + b must be greater than the square of c. However, for a right triangle, the Pythagorean Theorem states that if the lengths of the legs are a and b, and if the length of the hypotenuse is c, then a2 + b2 = c2, not a2 + b2 > c2. Therefore, since the Pythagorean Theorem is known to be correct, and since right triangles should adhere to the Triangle Inequality Theorem,

Answer 1

the Triangle Inequality Theorem must be incorrect.

What is wrong with Raj’s argument?
A)
The square of a + b is not equal to a2 + b2.
B)
One cannot assume that a, b, and c are all positive numbers.
C)
It’s not true that right triangles should adhere to the Triangle Inequality Theorem.
D)
It’s not true that according to the Triangle Inequality Theorem, a + b > c.