Math Problem Statement

If a figure is a rectangle, then it has 4 sides. Decide the truth value of each statement. If false, find a counterexample. Choose all that apply.

Solution

The statement in the image reads: "If a figure is a rectangle, then it has 4 sides." The task is to determine if this statement is true or false and select the appropriate answer from the options.

Analysis:

  • True: A rectangle is a quadrilateral, which means it has 4 sides. Therefore, this statement is true.

  • False - square: A square is a special type of rectangle, but it also has 4 sides. This does not provide a counterexample.

  • False - trapezoid: A trapezoid can have 4 sides, but it is not always a rectangle. However, this does not challenge the original statement since we are focusing on rectangles, not trapezoids.

  • False - triangle: A triangle has 3 sides, but a triangle cannot be a rectangle. Thus, this option does not apply.

Conclusion:

The correct choice is True because a rectangle, by definition, always has 4 sides.

Would you like more details or have any other questions?

Related Questions:

  1. What are the defining properties of a rectangle?
  2. Can a square be considered a rectangle? Why or why not?
  3. How do you distinguish between a rectangle and other quadrilaterals like a trapezoid?
  4. What is the difference between a rhombus and a rectangle?
  5. Can a rectangle ever be classified as a parallelogram?

Tip: Always ensure to check the definition of the shapes involved before determining the truth of a geometric statement.

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals

Formulas

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Theorems

Definition of a rectangle
Properties of quadrilaterals

Suitable Grade Level

Grades 3-5