1. Which of the following statements is false? *
1.A square is a rectangle whose adjacent sides are equal
2.A square is a rhombus whose one angle is a right angle.
3.The diagonals of a square bisect each other at right angles.
4.The diagonals of a square do not divide the whole square into four equal parts.
2. Which of the following statement is false? *
1.All the rectangles are parallelograms
2.All the squares are rectangles
3.All the parallelograms are rectangles
4.All the rhombuses are parallelograms
3. Which of the following statement is true? *
1.All the rectangles are squares
2.All the parallelograms are rhombuses
3.All the squares are rhombuses
4.Each trapezium is a parallelogram
4. Which of the following statement is true? *
1.All the rhombuses are squares
2.Each square is a parallelogram
3.Each parallelogram is a square
4.Each trapezium is a parallelogram
Answers
Answer:
1 (4)
2 (3)
3 (3)
4 (2)
Explanation:
1.
As diagonals of a square bisect each other, any one triangle formed by a diagonal will have the other diagonal as its median. Hence, that particular triangle is divided into two triangles of equal area. Similarly, all four triangles so formed will be of equal area, hence statement (4) is false.
2.
Rectangles are parallelograms with one angle as a right angle. However, all parallelograms do not have right angles. Hence, all rectangles are parallelograms but all parallelograms are not rectangles - statement (3) is false.
3.
A rhombus is a parallelogram with all sides equal. A square, in addition to having all sides equal, also has one angle as a right angle. Hence, a square possesses all characteristics of a rhombus and so statement (3) is true.
4.
A square has opposite sides parallel, all sides (opposite sides included) equal and all angles (opposite angles included) equal. Hence, a square has all characteristics of a parallelogram and so statement (2) is true.
TIP:
Make sure you know all properties of quadrilaterals thoroughly as that will help in such type of questions.
Good luck!
Answer:
1: 4
2: 3
3: 3
4: 2
hope it is helpful for you