The problem asks to construct point P on side AD of quadrilateral ABCD using a ruler and compass, where P is the intersection of AD and the folding line formed when side AB is folded to coincide with side BC. This means we need to construct the angle bisector of angle ABC.

1. Problem Description

The problem asks to construct point P on side AD of quadrilateral ABCD using a ruler and compass, where P is the intersection of AD and the folding line formed when side AB is folded to coincide with side BC. This means we need to construct the angle bisector of angle ABC.

2. Solution Steps

Step 1: Construct the angle bisector of angle ABC.

Place the compass at point B, and draw an arc that intersects both line segments AB and BC. Label these intersection points as E and F respectively.

Step 2: Using the same compass width as in step 1, or a different width, place the compass on point E and draw an arc in the interior of angle ABC. Then, place the compass on point F and draw an arc with the same width such that it intersects the arc previously drawn from point E. Label the intersection point of the two arcs as G.

Step 3: Draw a line segment from point B through point G. This line segment is the angle bisector of angle ABC.

Step 4: Extend the angle bisector until it intersects with side AD. The intersection point is P.

3. Final Answer

Point P is the intersection of the angle bisector of angle ABC and side AD.