Constructions and Tilings

When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below XY? Explore this through construction, and then justify your answer.

Is it necessary to construct the pairs of arcs above and below XY? Instead, can we construct both the pairs of arcs on the same side of XY? Explore this through construction, and then justify your answer.

While constructing one pair of intersecting arcs, is it necessary that we use the same radii for both of them? Explore this through construction, and then justify your answer.

Can you think of different methods to construct a 90° angle at a given point on a line using a rope?

Construct at least 4 different angles. Draw their bisectors.

What are the other angles that can be constructed using angle bisection? Can you construct 65.5° angle?

Come up with a method to construct the angle bisector using a rope.

Construct at least 4 different angles in different orientations without taking any measurement. Make a copy of all these angles.

Construct 4 pairs of parallel lines in different orientations.

Make your own arch designs.

Draw a line l and mark a point P anywhere outside the line. Construct a perpendicular to the given line l through P.