To determine if a triangle is a right triangle (i.e., has one 90-degree angle), you can use the following methods:
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Using the Pythagorean Theorem: If you know the lengths of all three sides of the triangle (let's say \(a\), \(b\), and \(c\), where \(c\) is the longest side), you can check if it satisfies the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] If this equation holds true, then the triangle is a right triangle.
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Using Trigonometry: If you know the measures of two angles, you can determine if the third angle is 90 degrees. For example, if you have angles \(A\) and \(B\), you can check if: \[ A + B = 90^\circ \] If true, then the triangle is a right triangle.
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Using Coordinates: If you plot the triangle on the coordinate plane, you can calculate the slopes of the sides. If two sides are perpendicular (one side has a slope of \(m_1\) and the other has a slope of \(m_2\)), they satisfy the condition: \[ m_1 \cdot m_2 = -1 \] This indicates that there is a right angle between those sides.
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Measuring Angles with a Protractor: If you directly measure the angles of the triangle using a protractor, you can confirm if one of the angles is 90 degrees.
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Visual Inspection: Sometimes, you may have an intuitive sense that a triangle looks like it has a right angle (for example, if it has a corner that appears to be a perfect corner). However, visual inspection should be paired with measured methods to confirm accuracy.
In summary, while visual inspections may give you a clue, the most reliable methods involve using the Pythagorean theorem, measuring using a protractor, or using coordinates and slopes.