Pregunta
If \( P \) represents the set of rhombi and \( Q \) the set of rectangles, then the set \( P \cap Q \) represents the set of (A) squares (B) trapezoids (C) parallelograms (D) quadrilaterals (E) rectangles
Ask by Parry Ayala. in Egypt
Mar 18,2025
Solución de inteligencia artificial de Upstudy
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The set \( P \cap Q \) represents the set of squares.
Solución
1. A rhombus is a quadrilateral with four congruent sides.
2. A rectangle is a quadrilateral with four right angles.
3. A quadrilateral that is both a rhombus and a rectangle must have four congruent sides and four right angles.
4. Such a quadrilateral is defined as a square.
Thus, the set \( P \cap Q \) represents the set of squares.
The correct answer is **(A) squares**.
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Simplifique esta solución Beyond the Answer
The set \( P \cap Q \) represents the set of shapes that are both rhombi and rectangles. The only type of quadrilateral that fits this criterion is a square. A square has all the properties of a rhombus (all sides equal) and all the properties of a rectangle (all angles right angles). So, the correct answer is (A) squares.
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