Question

use the compass and ruler to construct the bisector of the angle given below.

Explanation:

Step1: Set Compass on Vertex

Place the compass point on the vertex (the intersection point of the two angle sides). Draw an arc that intersects both sides of the angle. Let's call these intersection points \( A \) (on one side) and \( B \) (on the other side).

Step2: Arc from Point \( A \)

Without changing the compass width, place the compass point on \( A \) and draw an arc inside the angle.

Step3: Arc from Point \( B \)

Keep the compass width the same, place the compass point on \( B \) and draw another arc inside the angle. This arc should intersect the arc drawn from \( A \). Let's call the intersection point \( C \).

Step4: Draw the Bisector

Using the ruler, draw a line from the vertex of the angle through point \( C \). This line is the angle bisector, dividing the original angle into two equal angles.

Answer:

The angle bisector is constructed by following the steps: (1) Arc from vertex intersecting both sides, (2) Arcs from intersection points intersecting inside the angle, (3) Drawing a line from vertex through the intersection point of the two inner arcs. The final constructed bisector is a line that splits the given angle into two congruent angles.