To prove that a quadrilateral is a rectangle using slopes, you need to show that either pairs of opposite sides are parallel or that adjacent sides are perpendicular.
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Finding the slopes:
- The slope of a line is calculated using the formula \((y_2 - y_1) / (x_2 - x_1)\).
- From your provided slopes, we’ll assume that sides AD and DC correspond to the slopes given.
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Analyzing slopes:
- If you state side AD has a slope of "X" and side DC has a slope of "Y," we will need those specific values to determine if they’re parallel or perpendicular.
- Two lines are parallel if their slopes are equal (\( m_1 = m_2 \)).
- Two lines are perpendicular if the product of their slopes equals \(-1\) (\( m_1 \times m_2 = -1 \)).
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Given information:
- Unfortunately, you haven't provided the specific slopes for sides AD and DC. However, you provided possible responses that include pairs of slopes.
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Responses Analysis:
- If we take one of your responses, let’s analyze:
- Slope of AD = 2, Slope of DC = -2:
- These slopes are perpendicular since \(2 \times -2 = -4\), so this is incorrect as they should equal \(-1\).
- Slope of AD = 1, Slope of DC = -1:
- These slopes are perpendicular since \(1 \times -1 = -1\).
- Slope of AD = -2, Slope of DC = 2:
- Again, these slopes are perpendicular since \(-2 \times 2 = -4\), so this is also incorrect.
- Slope of AD = 2, Slope of DC = -2:
- If we take one of your responses, let’s analyze:
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Conclusion:
- To conclusively prove that the quadrilateral is a rectangle, you need to determine if both pairs of opposite sides are either parallel or if adjacent sides are perpendicular.
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Final Summary:
- Please confirm the specified slopes for sides AD and DC, and I can help determine if they help prove that the shape is a rectangle based on being parallel or perpendicular.
If you provide the accurate slopes for sides AD and DC, I can provide explicit conclusions regarding the conditions necessary for proving if the quadrilateral is a rectangle!