Home
Class 11
MATHS
Which of the following are statements ? ...

Which of the following are statements ?
Each square is a rhombus.

Text Solution

AI Generated Solution

The correct Answer is:
To determine whether the statement "Each square is a rhombus" is a statement and evaluate its truth value, we can follow these steps: ### Step 1: Understand the Definitions - **Rhombus**: A rhombus is a quadrilateral with all sides of equal length. Additionally, the opposite sides are parallel, and the diagonals bisect each other at right angles. - **Square**: A square is a specific type of rhombus where all angles are right angles (90 degrees). It also has all sides of equal length and opposite sides that are parallel. ### Step 2: Analyze the Statement The statement in question is "Each square is a rhombus." ### Step 3: Determine the Truth Value - Since a square meets all the criteria of a rhombus (equal sides, opposite sides parallel, and diagonals bisecting at right angles), we can conclude that every square is indeed a rhombus. ### Conclusion Therefore, the statement "Each square is a rhombus" is a true statement. ---
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise COMPETITION FILE (JEE-MAIN)|6 Videos
  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise CHAPTER TEST 14|12 Videos
  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise REVISION EXERCISE|8 Videos
  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise CHAPTER TEST 4|12 Videos
  • MOCK TEST

    MODERN PUBLICATION|Exercise SECTION - D|5 Videos

Similar Questions

Explore conceptually related problems

Which of the following statements is false for a square?

Write the converse statement of the following statement : If a quadrilateral is a rhombus then its diagonals are perpendicular bisectors of each other . Also state whether the converse statement is true .

State with reason whether the following statement , Every square is a rhombus is true or false.

Which of the following are statements ? Write the truth value of each : Square of a number is an even number.

Which of the following statements is false for a rhombus?

Which of the following statements are true and which are false ? The diagonals of a rhombus are equal.

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

Find out which of the following sentences are statements and which are not.Justify your answer: Every rhombus is a square.

Which of the following statements are true and which are false ? Every rhombus is a kite.