From the provided statements, we can analyze the logical implications:
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If a quadrilateral is a rhombus, then it is a parallelogram.
- This means all rhombuses are included in the set of parallelograms.
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If a quadrilateral is a parallelogram, then its opposite angles are congruent.
- This tells us that any parallelogram, which includes rhombuses, will have congruent opposite angles.
Now, let's evaluate the conclusions provided:
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Every quadrilateral is a rhombus.
- This statement is not true. A rhombus is a specific type of quadrilateral, but not all quadrilaterals are rhombuses.
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Every parallelogram is a rhombus.
- This statement is also not true. While all rhombuses are parallelograms, there are parallelograms that are not rhombuses (e.g., rectangles).
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Opposite angles of a rhombus are congruent.
- This statement is true. Since a rhombus is a type of parallelogram, it follows that its opposite angles are congruent.
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Opposite angles of a quadrilateral are congruent.
- This statement is not true for all quadrilaterals. Only specific types (e.g., parallelograms) have this property.
Based on the provided statements, the valid conclusion that can be drawn is: Opposite angles of a rhombus are congruent.
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