Question

try it! construct an angle bisector

1. how can you construct the angle bisector of ∠g?

(image of angle with vertex g and two rays)

Explanation:

Step1: Place compass at vertex \( G \)

Open the compass to a suitable width. Draw an arc that intersects both sides of \( \angle G \), let the intersection points be \( A \) (on one side) and \( B \) (on the other side).

Step2: Compass at \( A \), draw arc

With the same compass width, place the compass tip at \( A \) and draw an arc inside the angle.

Step3: Compass at \( B \), draw arc

Without changing the compass width, place the compass tip at \( B \) and draw another arc inside the angle. This arc should intersect the arc drawn from \( A \) at a point, say \( C \).

Step4: Draw ray from \( G \) to \( C \)

Using a straightedge, draw a ray starting at vertex \( G \) and passing through point \( C \). This ray \( \overrightarrow{GC} \) is the angle bisector of \( \angle G \), as it divides \( \angle G \) into two equal angles.

Answer:

To construct the angle bisector of \( \angle G \):

1. Place the compass at vertex \( G \), draw an arc intersecting both sides of the angle (at points \( A \) and \( B \)).
2. With the same compass width, draw arcs from \( A \) and \( B \) inside the angle, intersecting at point \( C \).
3. Draw ray \( \overrightarrow{GC} \); this is the angle bisector.