To construct a line segment equal to AB+CDAB+CD, you would first draw a line segment ABAB with a length of 3.6 cm and then draw a line segment CDCD with a length of 1.6 cm.

Then, you would place the endpoint of CDCD at the endpoint of ABAB, so they connect end to end. The resulting line segment would be the sum of the lengths of ABAB and CDCD.

Now, to measure the total length of the constructed line segment:

Total length=AB+CD=3.6 cm+1.6 cm=5.2 cmTotal length=AB+CD=3.6 cm+1.6 cm=5.2 cm

So, the total length of the constructed line segment is 5.2 cm.

To construct a perpendicular to a given line segment at a point on it, you can follow these steps:

1. Draw the given line segment.
2. Choose a point on the line segment where you want the perpendicular to pass through. Let's call this point PP.
3. With point PP as the center, draw a circle with any radius that intersects the line segment at two points, let's call them AA and BB.
4. Draw a straight line through points AA and BB. This line will be perpendicular to the given line segment at point PP.

Now, you have constructed a perpendicular to the given line segment at the chosen point PP.

To construct an angle of 60 degrees and bisect it, you can follow these steps using a compass and straightedge:

1. Start by drawing a straight line segment ABAB using the straightedge.
2. With AA as the center, draw an arc using the compass to create an angle of any size, let's say 60 degrees. Mark the intersection point with the line segment as CC.
3. Without changing the compass width, place the compass at point CC and draw an arc intersecting the first arc at point DD.
4. Draw a straight line segment connecting point CC to point DD. This line segment CDCD bisects the angle CABCAB, creating two 30-degree angles.

Now, you have constructed an angle of 60 degrees and bisected it into two 30-degree angles.

To draw an angle of 120° and then construct an angle of 105°, follow these steps:

1. Draw an Angle of 120°:

   • Use a protractor to draw a straight line (ray) and mark a point on it to represent the vertex of the angle.
   • Place the center of the protractor at the vertex and align the baseline of the protractor with the ray.
   • Mark a point at the 120° mark on the protractor.
   • Draw a line from the vertex to the marked point to complete the angle.

2. Construct an Angle of 105°:

   • Place the center of the protractor at the vertex of the 120° angle.
   • Align the baseline of the protractor with one side of the 120° angle.
   • Mark a point at the 105° mark on the protractor.
   • Draw a line from the vertex to the marked point to construct the 105° angle.

Now, you have both the 120° angle and the constructed 105° angle.

To draw triangle ABC and its perpendiculars from each vertex onto the opposite sides, follow these steps:

1. Draw triangle ABC:

   • Draw three non-parallel lines intersecting at points A, B, and C to form triangle ABC.

2. Draw perpendiculars from each vertex onto the opposite sides:

   • From vertex A, draw a line perpendicular to side BC. Label the point of intersection with side BC as D.
   • From vertex B, draw a line perpendicular to side AC. Label the point of intersection with side AC as E.
   • From vertex C, draw a line perpendicular to side AB. Label the point of intersection with side AB as F.

Now, you have triangle ABC with perpendiculars AD, BE, and CF drawn from vertices A, B, and C respectively onto the opposite sides BC, AC, and AB.

To determine if these perpendiculars are concurrent (passing through the same point), you can construct the altitudes of the triangle, which are known to be concurrent at the orthocenter.

If the perpendiculars AD, BE, and CF intersect at a single point, then they are concurrent, and that point is the orthocenter of triangle ABC. If they do not intersect at a single point, then they are not concurrent.

Please note that the concurrency of perpendiculars in a triangle depends on the specific properties of the triangle. In some cases, the perpendiculars may be concurrent, while in others, they may not be. You would need to verify this for the specific triangle you've drawn.