Math Problem Statement

If a figure is a rectangle, then it has 4 sides. Choose the correct truth value of the statement.

Solution

The statement in the image is: "If a figure is a rectangle, then it has 4 sides."

Let's break this down:

  1. True or False:

    • A rectangle is a type of quadrilateral, and by definition, a quadrilateral has 4 sides. So, the statement "If a figure is a rectangle, then it has 4 sides" is True.
  2. Counterexamples:

    • There are no valid counterexamples for this statement because all rectangles are quadrilaterals with exactly 4 sides. The options such as "False - square," "False - trapezoid," and "False - triangle" are not relevant counterexamples, as squares and trapezoids also have 4 sides, and triangles have 3 sides (so they don’t apply).

Thus, the correct answer to select here is True.

Would you like more details on rectangles or other geometric shapes?

Here are some related questions to deepen your understanding:

  1. What are the key properties that define a rectangle?
  2. How is a square related to a rectangle in terms of geometry?
  3. What are some other types of quadrilaterals besides rectangles?
  4. How can you classify a trapezoid in terms of its sides and angles?
  5. What makes a figure a polygon, and how do triangles differ from quadrilaterals?

Tip: Remember that a square is a special type of rectangle, but not all rectangles are squares!

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals
Rectangles

Formulas

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Theorems

Properties of quadrilaterals
Definition of a rectangle

Suitable Grade Level

Grades 6-8