use the compass and ruler to construct the bisector of the angle given below.
use the compass and ruler to construct the bisector of the angle given below.
Answer
Explanation:
Step1: Place compass at vertex
Put the compass tip on the angle's vertex (the intersection point of the two rays). Draw an arc that intersects both sides of the angle. Let's call the intersection points ( A ) (on one ray) and ( B ) (on the other ray).
Step2: Set compass to ( AB ) length
Without changing the compass width, place the compass tip on ( A ) and draw an arc inside the angle. Then place the compass tip on ( B ) and draw another arc inside the angle. These two arcs should intersect at a point, say ( C ).
Step3: Draw the bisector
Use the ruler (straightedge) to draw a line from the vertex of the angle through the intersection point ( C ). This line is the angle bisector.
Answer:
The angle bisector is constructed by following the steps of arc - drawing with the compass and then using the ruler to connect the vertex to the intersection of the arcs inside the angle. (Note: Since this is a construction problem, the final answer is the constructed angle bisector as per the above steps.)