Question

consider angle rst, where sr≅st. which instructions can be used to bisect the angle correctly? set a compasss width to half of the length of the line segment passing through point r and point t. place the compass at point r, and draw an arc in the exterior of ∠rst. place the compass at point r again at point r, and draw an arc in the interior of ∠rst. draw a segment connecting the two arcs. set a compasss width to half of the length of the line segment passing through point r and point t. place the compass at point r, and draw an arc in the interior of ∠rst. using a straightedge, draw a ray from point s to the segment connecting the arcs. set a compasss width to the length of st. place the compass at point r, and draw an arc in the interior of ∠rst. using a straightedge, draw a ray from point s through the intersection of the two interior arcs.

Explanation:

Step1: Recall angle - bisecting steps

To bisect an angle $\angle RST$, first set the compass width to an appropriate length (usually more than half - way across the angle). Place the compass at point $S$ and draw an arc that intersects both rays $SR$ and $ST$.

Step2: Draw second set of arcs

Place the compass at the intersection points on $SR$ and $ST$ (let's call them $A$ and $B$) and draw arcs in the interior of the angle. The intersection of these two new arcs is a point on the angle - bisector.

Step3: Draw the angle - bisector

Use a straightedge to draw a ray from point $S$ through the intersection of the two interior arcs.

The correct steps are: Set a compass's width to half of the length of the line segment passing through point $R$ and point $T$. Place the compass at point $R$, and draw an arc in the interior of $\angle RST$. Place the compass at point $T$, and draw an arc in the interior of $\angle RST$. Using a straightedge, draw a ray from point $S$ through the intersection of the two interior arcs.

Answer:

Set a compass's width to half of the length of the line segment passing through point $R$ and point $T$. Place the compass at point $R$, and draw an arc in the interior of $\angle RST$. Place the compass at point $T$, and draw an arc in the interior of $\angle RST$. Using a straightedge, draw a ray from point $S$ through the intersection of the two interior arcs.