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Start with two line segments and the included angle.
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| 1. Mark a point A that will be one vertex of the new triangle. |
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| 2. Draw a ray from point A.
This will become the side AB of the new triangle, so make it longer than AB. |
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| 3. Set the compasses' width to the length of the given side AB. |
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| 4. Set the compasses on A, and mark a point B on the ray just drawn. |
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| 5. With the compasses set to any convenient width, from the point A on the given angle,
draw an arc across both lines.. |
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| 6. Without changing the compasses' width, draw a similar sized arc at point A on the new triangle. |
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| 7. Set the compasses 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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| 8. Make a similar arc on the new triangle so it crosses the previous arc. |
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| 9. Draw a ray from A, through where the arcs intersect and onwards.
This will become side AC of the triangle so make it longer than AC. |
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| 10. Set the compasses' width to the distance AC. |
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| 11. With the compasses on A, make an arc across the second ray, creating point C. |
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| 12. Draw the line BC, the third side of the triangle |
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| Done, the triangle ABC has the desired two side lengths and included angle. |
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