Question

basic constructions

1. what is each construction?
2. order the steps used to bisect the angle below.

draw an arc centered at the vertex of the angle that intersects each side of the angle at points p and q.
draw the bisecting line from the vertex of the angle through point r.
draw two arcs of the same radius, one from point p and one from point q, so that they intersect at point r.

1. order the steps used to copy ∠a below.

with the compass tip at a, draw an arc intersecting both rays of ∠a. label the points of intersection b and c.
using the same compass setting and with the compass tip at d, draw an arc intersecting the ray at a point f.
using the same compass setting and placing the compass tip at f, draw an arc that intersects the previously drawn arc at a point e. use a straightedge to draw (overrightarrow{de}).
use a straightedge to draw a ray with a point d as its endpoint.
with the compass tip at c, open the compass to span to point b.

Explanation:

Step1: Identify the construction in 1st figure

It is constructing a perpendicular bisector of a line - segment.

Step2: Identify the construction in 2nd figure

It is constructing a congruent angle.

Step3: Identify the construction in 3rd figure

It is constructing an angle - bisector.

Step4: Order steps for bisecting an angle

1. Draw an arc centered at the vertex of the angle that intersects each side of the angle at points P and Q.
2. Draw two arcs of the same radius, one from point P and one from point Q, so that they intersect at point R.
3. Draw the bisecting line from the vertex of the angle through point R.

Step5: Order steps for copying an angle

1. Use a straightedge to draw a ray with a point D as its endpoint.
2. With the compass tip at A, draw an arc intersecting both rays of ∠A. Label the points of intersection B and C.
3. With the compass tip at C, open the compass to span to point B.
4. Using the same compass setting and with the compass tip at D, draw an arc intersecting the ray at a point F.
5. Using the same compass setting and placing the compass tip at F, draw an arc that intersects the previously drawn arc at a point E.
6. Use a straightedge to draw $\overrightarrow{DE}$.

Answer:

1. First figure: Perpendicular bisector of a line - segment; Second figure: Construction of a congruent angle; Third figure: Construction of an angle - bisector.
2. Steps for bisecting an angle:

• Draw an arc centered at the vertex of the angle that intersects each side of the angle at points P and Q.
• Draw two arcs of the same radius, one from point P and one from point Q, so that they intersect at point R.
• Draw the bisecting line from the vertex of the angle through point R.

1. Steps for copying an angle:

• Use a straightedge to draw a ray with a point D as its endpoint.
• With the compass tip at A, draw an arc intersecting both rays of ∠A. Label the points of intersection B and C.
• With the compass tip at C, open the compass to span to point B.
• Using the same compass setting and with the compass tip at D, draw an arc intersecting the ray at a point F.
• Using the same compass setting and placing the compass tip at F, draw an arc that intersects the previously drawn arc at a point E.
• Use a straightedge to draw $\overrightarrow{DE}$.