Question

making bisectors of angles and lines - complete the following problems: 1) bisect < xyz. 2) bisect line segment pq. 3) bisect < pqr.

Explanation:

Step1: Bisecting ∠XYZ

1. Place the compass at vertex Y.
2. Draw an arc that intersects rays YX and YZ at points A and B respectively.
3. Place the compass at point A and draw an arc inside the angle.
4. Without changing the compass width, place the compass at point B and draw another arc that intersects the previous arc. Let the intersection - point be C.
5. Draw the ray YC. Ray YC is the angle - bisector of ∠XYZ.

Step2: Bisecting line segment PQ

1. Place the compass at point P and open it to a radius greater than half of the length of PQ.
2. Draw arcs above and below the line segment PQ.
3. Without changing the compass width, place the compass at point Q and draw similar arcs above and below the line segment PQ, intersecting the previous arcs at two points (say M and N).
4. Draw the line MN. The line MN intersects PQ at its mid - point, thus bisecting the line segment PQ.

Step3: Bisecting ∠PQR

1. Place the compass at vertex Q.
2. Draw an arc that intersects rays QP and QR at points X and Y respectively.
3. Place the compass at point X and draw an arc inside the angle.
4. Without changing the compass width, place the compass at point Y and draw another arc that intersects the previous arc. Let the intersection - point be Z.
5. Draw the ray QZ. Ray QZ is the angle - bisector of ∠PQR.

Answer:

1. Ray YC bisects ∠XYZ.
2. The line MN bisects line segment PQ.
3. Ray QZ bisects ∠PQR.