Question

What is the construction that needs to be done to make a copy of ∠BAC?(1 point)ResponsesUsing a straight edge, construct a horizontal line from point P that intersects with the arc to find the middle of the angle.Using a straight edge, construct a horizontal line from point upper P that intersects with the arc to find the middle of the angle.Using a compass, measure the length from point B to point C. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.Using a compass, measure the length from point upper B to point upper C . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P .Using a compass, measure the distance from point Q to point B. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.Using a compass, measure the distance from point upper Q to point upper B . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P .Using a compass, measure the length from point A to point C. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.

Answer 1

To construct a copy of angle ∠BAC using a compass and straightedge, follow these steps:

1. Draw a Ray: Start by drawing a ray from point Q, which will be the vertex of the new angle.
2. Measure the Arc: Place the compass point on point A (the vertex of the original angle) and measure the distance to point B. This distance (AB) will be the radius for your first arc.
3. Draw Arc for Original Angle: With the compass still set to distance AB, draw an arc across both rays of angle ∠BAC.
4. Transfer Arc to New Ray: Without changing the width of the compass, place the compass point on point Q, and draw an arc that intersects the new ray.
5. Measure to Find Point: Now, keep the same compass width and place the compass point on point B (original angle). Draw a second arc to intersect with the first arc you drew in step 4.
6. Mark Intersection and Draw Line: Mark the point where these arcs intersect and label it. Then use a straightedge to draw a line from point Q through this new intersection point.

Therefore, the response to your question can best be summarized as follows:

• Using a compass, measure the length from point B to point C. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.

This response correctly reflects the necessary steps to construct an angle congruently.