The diagonals of a rhombus are perpendicular bisectors of each other. Using this information , construct a rhombus with diagonals 12cm and 7cm.

Question

Measure
A side of the rhombus
The smaller angle of the rhombus

Answer 1

To construct a rhombus with diagonals 12cm and 7cm, follow these steps:

1. Draw a horizontal line segment AB of length 12cm.
2. On AB, mark the midpoint M.
3. Draw a perpendicular line segment MC from M, with a length of 7cm.
4. Bisect line segment AB at point X.
5. Bisect line segment MC at point Y.
6. Connect points X and Y to form the rhombus.

To find the measurements:

1. To find the length of a side of the rhombus, measure the distance from point X to point Y. This distance will be equal to the length of a side of the rhombus. Let's say it measures s cm.
2. To find the smaller angle of the rhombus, measure the angle between either side and one of the diagonals (e.g., angle BXY). This angle will be the smaller angle of the rhombus.