Square

First we constructed perpendicular bisectors (KF and LJ) through points A and B. Then we drew circle A with a radius of AB, and circle B with radius AB (so the sides would be equal to segment AB). This showed us the height of the square. Next we drew circle K radius AB and circle L radius AB and connected KL. Lastly we connected ABKL to form a quadrilateral. We know this is a square because a square is a rhombus with all right angles. This can be a rhombus because of the parallel lines (which we know are parallel because each pair of parallel lines are perpendicular to the same line/lines). Secondly, we know that this is a square because angles A and B are 90 degrees (because they are made from perpendicular lines), so all angles are right angles. Lastly, we know each side is congruent because they are all radii of the same circle. These properties result in the quadrilateral ABKL being able to be classified as a rectangle and a rhombus, so, using the theorem “if a quadrilateral is a rectangle and a rhombus, then it’s a square”, quadrilateral ABKL can be classified as a square. (this shape can classify as a rectangle because of the right angles and the pairs of parallel lines, and can classify as a rhombus because of its congruent sides and parallel lines)