Question 4 of 12intermediate🔍 AnalyzeShort Answer2 marks

Is it possible to construct a 4-sided figure in which— all the angles are equal to 90° but opposite sides are not equal?

Correct Answer

No, it is not possible to construct a 4-sided figure where all angles are 90° but opposite sides are not equal.

Reasoning: In any quadrilateral with all four angles equal to 90°, the opposite sides must be equal in length. When all angles are right angles, the figure must be a rectangle. By definition, a rectangle has opposite sides equal. Any attempt to construct such a figure with unequal opposite sides will result in angles that are not all 90°.

Conclusion: ∴ Such a figure cannot be constructed.

Exercise: Construct | Q: 3 | (Page Page 11)
For More Understanding

Explanation

The chapter establishes that a rectangle has two properties: R1) Opposite sides are equal, and R2) All angles are 90°. These properties are interconnected. If all angles are 90°, the figure must be a rectangle, which automatically means opposite sides are equal. This is a fundamental geometric principle.

Solution Steps

  1. A quadrilateral with all angles = 90° must be a rectangle.

  2. A rectangle has opposite sides equal by definition.

  3. Therefore, opposite sides must be equal if all angles are 90°.

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