Consider the following statements:
Which is/are true?
(A) The sum of any two sides of a triangle is greater than the third side.
(B) The median of a triangle divides it into two triangles of equal area.
(C) The diagonals of a parallelogram bisect each other.
(D) The diagonals of a rhombus are equal and bisect each other.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (C) only
(A) The sum of any two sides of a triangle is greater than the third side. Correct. This is the triangle inequality: the straight side is the shortest path between its ends, so going round by the other two sides is always longer.
(B) The median of a triangle divides it into two triangles of equal area. Correct. A median joins a vertex to the midpoint of the opposite side, so the two triangles have equal bases and the same height, hence equal areas.
(C) The diagonals of a parallelogram bisect each other. Correct. This is a standard property of every parallelogram: the diagonals cut each other into halves.
(D) The diagonals of a rhombus are equal and bisect each other. Incorrect. The diagonals of a rhombus bisect each other at right angles, but they are not equal in general; they are equal only when the rhombus is a square.