Start with grouping the statements in all possible combinations and try to find an example for each group.
G
Practice makes perfect
We are given three statements.
I. &Opposite sides of parallelogram ABCD are parallel.
II. &Diagonals of parallelogram ABCD are perpendicular.
III. &Parallelogram ABCD is not a rhombus.
In order to identify which of the statements contradict each other, we will first group the statements in all possible combinations.
Next, we will try to find an example for each group. Let's start with Group A.
Group A
For this group, we are looking for a parallelogram whose diagonals are perpendicular. An example for this is a rhombus.
Therefore, statements I and II do not contradict each other.
Group B
For this group, we are looking for a parallelogram that is not a rhombus. Since they are both parallelograms, let's recall the definitions of rectangle and square.
Square: The opposite sides are parallel and have equal lengths.
Rectangle: The opposite sides are parallel and at least two of the sides are the same length.
Note that the above figures are parallelograms that are not rhombii. Therefore, statements I and III do not contradict each other.
Group C
If the diagonals of parallelogram are perpendicular, this parallelogram must be a rhombus. Therefore, it is not possible to give an example of a parallelogram and that meets these requirements. Statements II and III contradict each other. So, the correct option is G.
