To construct a copy of the angle ā BAC using a compass and straightedge, follow these steps:
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Draw a Base Line: Start by drawing a horizontal line (let's call it line PQ).
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Mark Point P: Place point P on that line where you want the vertex of the new angle to be located.
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Copy Angle Using Compass:
- Using your compass, measure the length of segment BC (from point B to point C) in angle ā BAC.
- With the compass still set to that length, place the pointed end on point P and draw an arc across line PQ and above.
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Mark the Arc Intersection: Mark the point where the arc intersects line PQ as point R.
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Find the Length for Point Q: Now, keeping your compass at the same width, place the pointed end on point A (the original vertex of angle BAC) and draw an arc in the same way to capture the angle's opening.
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Intersect the Arcs: Finally, using the same compass width (the distance between B and C), place the compass on point R (the intersection you marked above) and draw a second arc that intersects with the first arc drawn above point P (let's name that intersection point S).
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Complete the Angle: Draw a straight line from point P through point S. This will create an angle ā PQR that is congruent toā BAC.
By following these steps, you will successfully construct a copy of the angle ā BAC at the new location on point P.