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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- 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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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