Answer:
Here are the steps to construct each named quadrilateral with the given diagonal:
1. Parallelogram WXYZ given diagonal WY
- Draw a line segment WY of any length and mark its midpoint M.
- Draw a circle with center M and radius WY. This circle will intersect the line segment WY at two points, W and Y.
- Choose any point X on the circle that is not on the line segment WY. Draw a line segment WX.
- Draw another circle with center X and radius WX. This circle will intersect the first circle at two points, X and Z.
- Draw a line segment ZY to complete the parallelogram WXYZ.
- You can verify that WXYZ is a parallelogram by checking that opposite sides are parallel and equal in length, and opposite angles are equal.
2. Rhombus RHOM given diagonal RO
- Draw a line segment RO of any length and mark its midpoint N.
- Draw a perpendicular bisector of RO through N. This line will be the other diagonal of the rhombus.
- Choose any point H on the perpendicular bisector such that NH = NR. Draw a line segment RH.
- Draw a circle with center H and radius RH. This circle will intersect the line segment RO at two points, R and O, and the perpendicular bisector at two points, H and M.
- Draw a line segment MO to complete the rhombus RHOM.
- You can verify that RHOM is a rhombus by checking that all sides are equal in length, and opposite angles are equal.
3. Kite KITE given diagonal KT
- Draw a line segment KT of any length and mark its midpoint L.
- Draw a perpendicular bisector of KT through L. This line will be the other diagonal of the kite.
- Choose any point I on the perpendicular bisector such that IL < KL. Draw a line segment IT.
- Draw a circle with center I and radius IT. This circle will intersect the line segment KT at two points, T and E.
- Draw a line segment KE to complete the kite KITE.
- You can verify that KITE is a kite by checking that adjacent sides are equal in length, and one pair of opposite angles are equal.
Explanation: