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Exploring Parallelograms

In this investigation you will discover some special properties of parallelograms. A parallelogram is a quadrilateral whose opposite sides are parallel.

Sides and Angles of a Parallelogram

Use the interactive image above to answer the following questions.

Sides of a Parallelogram

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

Marca todas las que correspondan
  • A
  • B
  • C
Revisa tu respuesta (3)

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

Marca todas las que correspondan
  • A
  • B
  • C
Revisa tu respuesta (3)

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

Uncheck the opposite sides boxes by clicking on them again. This will hide the lengths.

Angles of a Parallelogram

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

Marca todas las que correspondan
  • A
  • B
  • C
Revisa tu respuesta (3)

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

Marca todas las que correspondan
  • A
  • B
  • C
Revisa tu respuesta (3)

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

Properties of Parallelograms.

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

Diagonals of a Parallelogram

Diagonals

Now we are going to look at the diagonals of a parallelogram. These are the segment and . We will do this using the interactive image above.

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

Marca todas las que correspondan
  • A
  • B
Revisa tu respuesta (3)

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?

Uncheck the box next to show length.