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Start with two line segments and the included angle.
The given angle is only there to indicate the measure of the the angle.
The lines making up the given angle have random lengths that have no significance in the construction.
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| 1. Mark a point A that will be one vertex of the new triangle. |
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| 2. the compass width to the length of the segment AB. |
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| 3. With the compass point on A, make an arc near the future vertex B of the triangle. |
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| 4. Mark a point B on this arc. Then draw the line AB. This will be one side of the new triangle. |
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| 5. Set the compass width to the length of the given side AC. |
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| 6. With the compass on A in the new triangle, make an arc roughly where the third point C will go.
The point C will be somewhere along this arc; the next steps will establish exactly where by copying the given angle. |
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| 7. With the compass set to any convenient width, from the point A on the given angle, draw an arc across both lines. |
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| 8. Without changing the compass width, draw an arc at point A on the new triangle.
The arc must cross AB and also cross the future side of the triangle. |
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| 9. Set the compass to the arc width at the given angle A.
This the distance between the points where the arc intersects the sides of the angle. |
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| 10. Near point A draw an arc in a similar position so it crosses the arc drawn earlier.
This, in effect, 'copies' the measure of the angle at P to the angle at A. |
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| 11. Draw a line from A through the point where the arcs intersect to meet the outer arc.
we now know where point C is along this arc. |
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| 12. Draw the line BC, the third side of the triangle |
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| 13. Done. The blue triangle ABC has the measures of the two sides AB and AC and the included angle desired. |
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