Write the instructions in different words, but doing the same constructions and detailed like you are teaching a 5th grader how to do it.

Copy an angle

Goal: Construct a copy of the given angle BAC.

->

/ B

/

/

A_/______________________ ->C

Step 1: Mark a point P to be the vertex of the new angle.

Step 2: Draw a ray PQ in any direction and in any length. This will be one side of the new angle.

Step 3: Set the compass point on A and adjust it to any convenient width.

Step 4: Draw an arc across both sides of the angle, creating points J and K.

Step 5: Move the compass to P and draw a similar arc, crossing PQ at M.

Step 6: Set the compass on K and set its width to J.

Step 7: Move the compass to M and draw an arc crossing the first, creating point L.

Step 8: Draw a ray PR from P through L.

Done. The angle RPQ has the same measure as BAC.

Copy an angle bisector

Goal: Construct a line which bisects the angle PQR.

Step 1: Place the compass point on the angle's vertex.

Step 2: Set the compass to any convenient width.

Step 3: Draw an arc across each leg.

Step 4: Compass can be adjusted at this point if desired.

Step 5: From where an arc crosses a leg, make an arc in the angle's interior.

Step 6: Without changing the compass width, repeat for the other leg.

Step 7: Draw a line from Q to where the arcs cross.

Done. The line just drawn bisects the angle PQR.

Construct an equilateral triangle

The line segment AB is given. (Vertical)

Goal: Construct an equilateral triangle whose side length is AB.

Step 1: Mark a point P that will become one vertex of the triangle.

Step 2: Set the compass width to the desired length AB.

Step 3: From P, draw an arc near both the other vertices (corners).

Step 4: Mark a point Q on either arc to be the next vertex.

Step 5: Without changing the width, move to Q and draw an arc across the other, creating R.

Step 6: Draw threee lines linking P, Q, and R.

Done. The equilateral triangle PQR has a side length equal to AB.

Construct a perpendicular bisector

Goal: Construct the perpendicular bisector of the given line segment PQ.

Step 1: Place the compass point on one end of the line.

Step 2: Adjust the compass to just over half the line length.

Step 3: Without adjusting the compass width, draw an arc on each side of the line.

Step 4: Without changing the compass width, repeat for the other end of the line.

Step 5: Draw a straight line between the two arc intersections.

Done. The line is the perpendicular bisector of PQ.

Construct a perpendicular line at a given point on a line

Goal: Construct a line perpendicular to the given line at the point K on that line.

Step 1: With the compass on K, set it to a medium width.

Step 2: Draw an arc on each side of K using that compass width, creating points P and Q.

Step 3: With the compass on P, set its width to about halfway between K and Q.

Step 4: Draw an arc on one side of the line.

Step 5: Without changing the width, repeat from point Q, creating point R.

Step 6: Draw a line from K to R.

Done. The line KR is perpendicular to PQ at K.

Construct a perpendicular line through a point NOT on a line

Goal: Construct a line perpendicular to the given line, that passes through point R.

A line is given, and point R is above it.

Step 1: Place the compass point on R.

Step 2: Adjust compass width to beyond the line.

Step 3: Draw two arcs across the line, creating points P and Q.

Step 4: From each point P, Q, draw an arc below the line so they cross.

Step 5: Draw a line from R to where the arcs intersect.

Done. The new line is perpendicular to PQ and passes through R.

Construct a line parallel to a given line

Goal: Construct a line parallel to PQ that passes through given point R.

There is a line segment with the points P and Q, and they are not the endpoints but each one is close to each end of the line segment. R is above the line segment, and is closer to P.

Step 1: Draw a line through R and across PQ at an angle, creating point J.

Step 2: With the compass width about half JR, and the point on JR draw an arc across both lines.

Step 3: Using the same compass width, repeat at point R.

Step 4: Set the compass width to the lower arc.

Step 5: Move the compass to the upper arc. Mark off an arc to make point S.

Step 6: Draw a straight line through R and S.

Done. The line RS is parallel to PQ.

Construct a square given one side

Goal: Construct a square where the side is a given length AB.

There is a line segment with the endpoints AB.

Step 1: Extend the line AB to the right.

Step 2: Draw an arc on each side of B using any compass width. Label these F and G.

Step 3: With the compass on G and any width, draw an arc above B.

Step 4: Without changing the width, repeat from point F, creating point H.

Step 5: Draw the perpendicular from B through H.

Step 6: Set the compass on A and set its width to the distance AB.

Step 7: Make an arc above A.

Step 8: Move the compass to B and make an arc above B, creating point C.

Step 9: Move the compass to C and make an arc left of C, creating point D.

Step 10: Draw the line segments CD and DA.

Done. ABCD is a square with the given side length.