Question

25 points

Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals.

Answer 1

To construct the parallelogram ABCD, follow these steps:

1. Draw a line segment AB of length 5 cm.
2. From point A, draw a perpendicular line segment AD of length 5 cm.
3. Draw a ray from point A, making an angle of 120 degrees with AB. Label the intersection of this ray and AD as point S.
4. Draw a line through point S parallel to AB, and label the intersection with the extension of AD as point C.
5. Draw a line through point B parallel to AD, and label the intersection with the extension of AB as point D.
6. The parallelogram ABCD is formed by connecting points A, B, C, and D.

The diagram of the parallelogram ABCD is shown below:

D - - - - -C

/ |

/ |

A - - - - - - - B

Note that AB is parallel to CD and AD is parallel to BC, and opposite sides of the parallelogram are congruent.