Exploring Parallelograms

Click the box next to Opposite Sides 1. What do you notice about the lengths of and (denoted by AC and BD)?

Click the box next to Opposite Sides 2. What do you notice about AB and CD?

Now move around vertices A, C, and D. Does the previous observations remain true?

Click on the box next to Opposite Angles 1. What do you notes about the measures of and (denoted by and )?

Click on the box next to Opposite Angles 2. What do you notice about and ?

Now move around vertices A, C, and D. Does the previous observations remain true?

The previous observations display two properties of parallelograms. What do you think these two properties are?

Click on the boxes next to Diagonal BC, Diagonal AD, and Show Length. Which of the following seems to be true?

Now move around vertices A, C, and D. Does the previous observations remain true?

This displays another property of parallelogram. What do you think this property is?

Use either vertex A, C, or D to make between and . Look at side lengths AB and BD. Are they equal?

Use either vertex A, C, or D to make between and . Look at side lengths AB and BD. Are they equal.

Click on the box next to Show Side Lengths. See if you can figure out what the definition of a rhombus is. A parallelogram where all four sides are _____________.

Now click on the box next to Show Diagonals. What kind of angle is ?

What does that mean about and ? (Please answer this question in a full sentence.)

Remember our observation about the intersection of the diagonals in the previous interactive image. Finish this sentence. The diagonals in a parallelogram are perpendicular if and only if it is a ________________.