Question

Inverse of the statement "If the triangle with side lengths $a,b,c$ is a right triangle, then $a^2+b^2=c^2$.

• A. If $a^2+b^2\ne c^2$ then the triangle with side lengths $a,b,c$ is not a right triangle.
• B. If $a^2+b^2=c^2$ then the triangle with side lengths $a,b,c$ is a right triangle.
• C. If the triangle with side lengths $a,b,c$ is a not right triangle, then $a^2+b^2\ne c^2$.
• D. None of the above.

Answer 1

Answer: (C)

If the triangle with side lengths $a,b,c$ is a not right triangle, then $a^2+b^2\ne c^2$.

Given,

If the triangle with side lengths $a,b,c$ is a right triangle, then $a^2+b^2=c^2$

This is of the form $p\to q$

$p$: If the triangle with side lengths $a,b,c$ is a right triagle.

$q:a^2+b^2=c^2$

Inverse of $p\to q$ is $\sim p\to \sim q$

$\Rightarrow$ If the triangle with side lengths $a,b,c$ is not a right triangle, then $a^2+b^2=c^2$.