Rhombus vs Square Properties: Analyzing Their Geometric Relationship

Given the rhombus:

Is every square a rhombus?

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Step-by-step video solution

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00:00 Is every square a rhombus
00:04 Opposite sides are parallel in a square
00:21 In a square all sides are equal
00:29 A quadrilateral with parallel and equal opposite sides is a parallelogram
00:34 A parallelogram with a pair of equal adjacent sides is a rhombus
00:40 Therefore every square is also a rhombus
00:47 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Given the rhombus:

Is every square a rhombus?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the properties of a rhombus.
  • Step 2: Identify the properties of a square.
  • Step 3: Analyze if the properties of a rhombus are met by a square.

Let's work through each step:

Step 1: A rhombus is defined as a quadrilateral where all four sides have equal length.
Step 2: A square is a quadrilateral with all four sides of equal length, and all four angles are 90 degrees.

Step 3: Since both definitions include having all sides of equal length, every square meets this condition of a rhombus. Furthermore, while a square has additional properties like equal angles, it doesn't negate it being a rhombus.

Therefore, every square satisfies the definition of a rhombus.

Concluding, the statement "Every square is a rhombus" is True.

3

Final Answer

True

Practice Quiz

Test your knowledge with interactive questions

Look at the following rhombus:

Are the diagonals of the rhombus parallel?

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