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Which of the following statements are tr...

Which of the following statements are true and which are false ?
Every square is a parallelogram.

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To determine whether the statement "Every square is a parallelogram" is true or false, we can analyze the properties of both shapes step by step. ### Step 1: Define a Parallelogram A parallelogram is a quadrilateral with the following properties: - Opposite sides are equal in length. - Opposite angles are equal. - The diagonals bisect each other. ### Step 2: Define a Square A square is a special type of quadrilateral that has the following properties: - All four sides are equal in length. - All four angles are equal (each measuring 90 degrees). - The diagonals are equal in length and bisect each other at right angles. ### Step 3: Compare Properties 1. **Opposite Sides**: - In a parallelogram, opposite sides are equal. - In a square, since all sides are equal, opposite sides are also equal. - **Conclusion**: This property holds true for both shapes. 2. **Opposite Angles**: - In a parallelogram, opposite angles are equal. - In a square, all angles are equal (90 degrees), hence opposite angles are also equal. - **Conclusion**: This property holds true for both shapes. 3. **Diagonals**: - In a parallelogram, the diagonals bisect each other. - In a square, the diagonals also bisect each other and are equal in length. - **Conclusion**: This property holds true for both shapes. ### Step 4: Conclusion Since all properties of a parallelogram are satisfied by a square, we can conclude that: - **Statement**: "Every square is a parallelogram" is **True**. ### Final Answer True, every square is a parallelogram. ---
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RS AGGARWAL-PARALLELOGRAMS-Exercise 16A
  1. In the adjacent figure , ABCD is a parallelogram and line segments AE...

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  2. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respecti...

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  3. In the given figure ABCD is a square . Find the measure of angleCAD.

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  4. The sides of a rectangle are in the ratio 5 : 4 and its perimeter is 9...

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  5. Name each of the following parallelograms. The diagonals are equal ...

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  6. Name each of the following parallelograms. The diagonals are equal ...

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  7. Name each of the following parallelograms. The diagonals are unequa...

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  8. Name each of the following parallelograms. All the sides are equal a...

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  9. Name each of the following parallelograms. All the sides are equal ...

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  10. Name each of the following parallelograms. All the angles are equal ...

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  11. The diagonals of a parallelograms are equal .

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  12. Which of the following statements are true and which are false ? The...

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  13. Which of the following statements are true and which are false ? The...

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  14. Which of the following statements are true and which are false ? Eve...

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  15. Which of the following statements are true and which are false ? Eve...

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  16. Which of the following statements are true and which are false ? Eve...

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  17. Is Every square a rhombus.

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  18. Which of the following statements are true and which are false ? Eve...

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  19. Which of the following statements are true and which are false ? Eve...

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  20. Which of the following statements are true and which are false ? Eve...

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