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To construct the bisector of ∠A (angle at point A) from the given diagram, follow these steps:

1. **Place the compass at point A**, and draw an arc that intersects both rays \( \overrightarrow{AB} \) and \( \overrightarrow{AC} \) at two points. Let these intersection points be called \( P \) (on \( \overrightarrow{AB} \)) and \( Q \) (on \( \overrightarrow{AC} \)).

2. **From points P and Q**, use the same compass width and draw two arcs that intersect each other. The intersection of these arcs will be a point that lies on the bisector of the angle.

3. **Draw a ray** from point A through the intersection point of the arcs. This ray is the angle bisector of \( \angle A \).

This process will result in a ray that divides the angle \( \angle A \) into two equal parts.

Would you like me to break down any of the steps or provide further details?

Here are 5 related questions to deepen your understanding:
1. How can we verify that the constructed bisector divides the angle equally?
2. What is the difference between bisecting an angle and bisecting a line segment?
3. Can an angle bisector be constructed using only a ruler, without a compass?
4. How does an angle bisector relate to the incenter of a triangle?
5. What is the significance of congruent angles when constructing bisectors?

**Tip:** When using a compass for construction, always keep the compass width consistent between steps to ensure accuracy in the intersection points.

Learn how to construct the bisector of angle ∠A using a compass and straightedge. Follow a step-by-step guide to bisect the angle, ensuring the compass width remains consistent for accuracy. Ideal for students in Grades 7-9 studying basic geometric constructions.

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