Question

Which of the following is not true for a parallelogram?
A) Opposite sides are equal
B) Opposite angles are equal
C) Opposite angles are bisected by diagonals
D) Diagonals bisect each other

Answer 1

Hint: According to Euclidean geometry, a parallelogram is a simple quadrilateral (four sided polygon) with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Complete answer:
We are given four properties of a parallelogram , and we need to determine which of the given properties is not true.
Consider the first option, which states that for a parallelogram, opposite sides are equal.
According to the definition of the parallelogram by Euclidean geometry, it is formed by the intersection of a pair of parallel lines, and a pair of parallel lines always have equal distance between them at any point of time. If the parallel lines cut another pair of parallel lines, then the formed quadrilateral will always have equal opposite sides. Hence the statement that the opposite sides are equal is correct.
Now, consider the second option, which states that for a parallelogram, opposite angles are equal.
Since, it is already shown that parallelogram has equal opposite sides, and we also know that for any quadrilateral which have equal opposite sides have equal opposite angles. Hence this statement is correct.
Consider the third option, which states that for a parallelogram, opposite angles are bisected by diagonals.
We know that parallelograms have equal opposite sides and equal opposite angles. If we draw the diagonals by joining the opposite vertices in a parallelogram, then we cannot say that diagonals bisect the opposite angles. The diagonals bisect each other, but don not bisect the angles. Hence, this statement is not correct.
Now, consider the fourth option, which states that for a parallelogram, diagonals bisect each other.
For a parallelogram, it is the property of the parallelogram that the diagonals bisect each other. So, the given statement is correct.
Thus, we get that only the third statement is not correct, hence the solution is option (C) Opposite angles are bisected by diagonals.

Therefore, the correct option is C

Note: A quadrilateral is a polygon in Euclidean plane geometry with four edges and four vertices. It is categorized into square, parallelogram, trapezoid, rectangle, rhombus based on the various properties.