In these lessons, we will learn

### Construct A Parallelogram given sides and angle

**How to construct a parallelogram with a given angle and certain side lengths?**

Example: Construct a parallelogram with side lengths c and d and with a 45° angle.**How to construct a parallelogram, using two lengths and one angle provided?**

Step 1: Make a copy of the given angle.

Step 2: Make a copy of the lengths for each side.

Step 3: Use the compass to mark the fourth vertex.### Construct a Parallelogram given its diagonals

This video shows how to construct a parallelogram given the lengths of its diagonals, using the property that diagonals of a parallelogram bisect each other. An infinite number of parallelograms are possible.

Example: Construct a parallelogram ABCD given the diagonals AC and BD.

Step 1: Bisect AC and BD.

Step 2: Draw a circle with the radius equals to 1/2 of AC.

Step 3: Draw a concentric circle with the radius equals to 1/2 of BD.

Step 4: Mark two points that will form the diameter on the bigger circle.

Step 5: Mark two points that will form the diameter on the smaller circle.

Step 6: Join the four points to form the parallelogram.**How to construct a parallelogram using the intersecting diagonals property of a parallelogram?**

The diagonals of a parallelogram bisect each other.

### How to construct a square given the length of its diagonal?

The following video shows how to construct a square with a compass and straight edge given the length of a diagonal.
**How to construct a square using a diagonal?**
### How to construct a square given its side?

The following video shows how to construct a square given the length of one side.
**How to construct a square given the length of one side?**
Two methods are shown.
### How to construct a rectangle?

How to draw a Rectangle Using a Compass and Straight Edge, and perpendicular bisector constructions.
Construct a rectangle with compass and straight edge.

Step 1: Construct two perpendicular segments.

Step 2: Mark off congruent sides.

Step 3: Check for 4 right right angles.

Step 4: Check that the diagonals are equal in lengths.

- how to construct a parallelogram given the lengths of its sides and an angle
- how to construct a parallelogram given the lengths of its diagonals
- how to construct a square given the length of the diagonal.
- how to construct a square given the length of one side.
- how to construct a rectangle

Example:

Construct a parallelogram ABCD with sides AB = 4 cm and AD = 5 cm and angle A = 60˚.

Solution:

Step 1: Construct a line segment AB = 4 cm. Construct a 60˚ angle at point A.

Step 2: Construct a line segment AD = 5 cm on the other arm of the angle. Then, place the sharp point of the compasses at B and make an arc 5 cm above B.

Step 3: Stretch your compasses to 4 cm, place the sharp end at D and draw an arc to intersect the arc drawn in step 2. Label the intersecting point C. Join C to D and B to C to form the parallelogram ABCD.

Example: Construct a parallelogram with side lengths c and d and with a 45° angle.

Step 1: Make a copy of the given angle.

Step 2: Make a copy of the lengths for each side.

Step 3: Use the compass to mark the fourth vertex.

Example: Construct a parallelogram ABCD given the diagonals AC and BD.

Step 1: Bisect AC and BD.

Step 2: Draw a circle with the radius equals to 1/2 of AC.

Step 3: Draw a concentric circle with the radius equals to 1/2 of BD.

Step 4: Mark two points that will form the diameter on the bigger circle.

Step 5: Mark two points that will form the diameter on the smaller circle.

Step 6: Join the four points to form the parallelogram.

The diagonals of a parallelogram bisect each other.

Step 1: Construct two perpendicular segments.

Step 2: Mark off congruent sides.

Step 3: Check for 4 right right angles.

Step 4: Check that the diagonals are equal in lengths.

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