Question

a. place the steps in order to construct a segment cd congruent to ab using only a compass and straightedge:
□ without changing the compass width, place the compass on point c.
□ draw line - segment cd using a straightedge.
□ set the compass on point a and adjust the width to point b.
□ draw an arc near the area where point d will lie.

b. work with your partner to order the nine steps for copying ∠fgh. the first and last step are in the correct position.

1. draw a point and label it x. then, draw a ray starting at point x in any direction. label the ray xz.

set the compass’ point on point a and adjust the compass’ width to point b.
without changing the compass’ width, place the compass’ point on y and draw a similar arc to create point w where the two arcs meet.
set the compass’ point on point g and adjust the compass’ width to any width.
without changing the compass’ width, place the compass’ point on x and draw a similar arc. label the point where the arc and xz intersect point y.
label the point where the arc crosses gf as point a.
label the point where the arc crosses gh as point b.
draw an arc across both rays of ∠fgh.

1. draw xw using a straightedge.

Explanation:

Step1: Set compass width

Set the compass on point A and adjust the width to point B.

Step2: Transfer compass width

Without changing the compass width, place the compass on point C.

Step3: Draw arc

Draw an arc near the area where point D will lie.

Step4: Draw segment

Draw line - segment CD using a straightedge.

For part b:

1. Draw a point and label it X. Then, draw a ray starting at point X in any direction. Label the ray XZ.
2. Set the compass’ point on point G and adjust the compass’ width to any width.
3. Draw an arc across both rays of ∠FGH.
4. Label the point where the arc crosses GF as point A.
5. Label the point where the arc crosses GH as point B.
6. Without changing the compass’ width, place the compass’ point on X and draw a similar arc. Label the point where the arc and XZ intersect point Y.
7. Set the compass’ point on point A and adjust the compass’ width to point B.
8. Without changing the compass’ width, place the compass’ point on Y and draw a similar arc to create point W where the two arcs meet.
9. Draw XW using a straightedge.

Answer:

a. 3rd: Set the compass on point A and adjust the width to point B.
1st: Without changing the compass width, place the compass on point C.
4th: Draw line - segment CD using a straightedge.
2nd: Draw an arc near the area where point D will lie.
b. 2: Set the compass’ point on point G and adjust the compass’ width to any width.
3: Draw an arc across both rays of ∠FGH.
4: Label the point where the arc crosses GF as point A.
5: Label the point where the arc crosses GH as point B.
6: Without changing the compass’ width, place the compass’ point on X and draw a similar arc. Label the point where the arc and XZ intersect point Y.
7: Set the compass’ point on point A and adjust the compass’ width to point B.
8: Without changing the compass’ width, place the compass’ point on Y and draw a similar arc to create point W where the two arcs meet.