In this lesson, we are going to investigate quadrilaterals that have unique characteristics.

Why study quadrilaterals? Look at the world around you. There are quadrilaterals everywhere. They are used in designs in architecture, designs in fabrics, designs in floors, and countless other ways. Knowing how to classify quadrilaterals will help you better understand the properties of each type of quadrilateral.

A quadrilateral is a plane figure that has four sides. However, a quadrilateral with two pairs of opposite sides that are parallel is a parallelogram.

Look at the parallelogram below and to the right. Notice the markings on each pair of opposite sides. Segments with the same markings are parallel to each other.

Using this applet http://www.geogebratube.org/student/b74601#material/35725 CCSS IP Math II 5.7.2:

1. Move the slider to the right slowly down.
2. Notice the measures of interior angles of the parallelogram.
3. Once the slider has gotten to the bottom, move the points to create a new parallelogram and repeat several times. Interactive roll-over image. Assistance may be required.

In your notes, answer the following:

• Describe the measures of the opposite angles of the parallelogram, angles 4, 9, 7 and 14, as you change the parallelogram.  
  
  Interactive popup. Assistance may be required. Check Your Answer Angles 4 and 9 are congruent and angles 7 and 14 are congruent. Opposite angles are congruent.
  
  
• Find the sum of the angles of the parallelogram. Do the sums change when sides of the parallelogram change?
  
  Interactive popup. Assistance may be required. Check Your Answer The sum of the angles of a parallelogram is 360. The sum of the angles never change.
  
  
• Find the sum of two adjacent angles of the parallelogram. Repeat with the next two angles.
  
  Interactive popup. Assistance may be required. Check Your Answer The sum of any two adjacent angles is 90.

Complete the following conjectures about parallelograms in your notes. Move your mouse pointer over each blank to see possible responses.

Using this applet, http://www.mathopenref.com/parallelogram.html, move the different vertices one at a time noting the similarities and differences in the parallelograms formed.

In your notes, answer the following:

• Compare and contrast the sides of the parallelograms as the lengths of the sides change.
  
  Interactive popup. Assistance may be required. Check Your Answer Opposite sides are always parallel and congruent.
  
  
• Formulate the Parallelogram Opposite Sides Conjecture: The opposite sides of a parallelogram are _____.
  
  Interactive popup. Assistance may be required. Check Your Answer congruent

Interactive roll-over image. Assistance may be required.

Using this applet, http://www.mathopenref.com/parallelogramdiags.html, move the vertices individually and observe the diagonals of the parallelogram.

In your notes, answer the following:

• Describe the diagonals of a parallelogram.
  
  Interactive popup. Assistance may be required. Check Your Answer Diagonals of a parallelogram always bisect each other.
  
  
• Formulate the Parallelogram Diagonals Conjecture: The diagonals of a parallelogram ______.
  
  Interactive popup. Assistance may be required. Check Your Answer bisect

Complete the following conjectures about parallelograms in your notes. Move your mouse pointer over each blank to see possible responses.