Question

Which of the following statements is NOT true about triangles?

A. The sum of interior angles in any triangle is always equal to 180 degrees

B. The square of the hypotenuse of a right-angle triangle equals the sum of the squares of the other two sides

C. The ratio of a side of a plane triangle to the sine of the opposite angle is the same for all three sides

D. The ratio of a sine of an angle of a plane triangle to the opposite side is the same for all three angles

E. None of the above

Answer 1

For the given question the correct answer is option 'C'.

Explanation:

For a plane triangle we have:

1) Sum of the all the interior angles is 180 degrees. Hence option 'A' is correct.

2) For a right angled triangle from Pythagoras theorem we know that
`H^2=a^2+b^2`

where,

H is the hypotenuse of the triangle

a,b are the sides of the right angled triangle

hence the option 'B' is also correct

3) For any triangle ABC we know that

`(sin(A))/(BC)=(sin(B))/(AC)=(sin(C))/(AB)=constant`

hence option 'D' is also correct.

Thus only incorrect answer among the given option is 'C'.