# Pattern block star challenge

Pattern block star challenge: find the angles of a trapezoid, triangle, parallelogram, and see if they make a perfect circle.

What are the angles of all the shapes and lengths of their sides?

Directions

Find the angles of all the shapes, draw them below, and label them.

Work area:

The angles of the orange square.

The angles of the red trapezoid.

The angles of the green triangle.

The angles of the white parallelogram.

Write an arguement for one the following conjectures:

The pattern blocks don't fit together precisely, because the blocks aren't made precisely enough for the shapes to fit together precisely.

or

They pattern blocks are made okay. Howver, it's not possible to put those white parallelograms into a circle, because their angles can't add up to 360 degrees.

Hints:

Use what you know about shapes, label the angles you know (square, equilateral triangle, ...) and reason from one to another to a circle.

More star pattern challenges:

• Verify if the orange red circle adds up to 360 degrees.
• Verify if the green white circle adds up to 360 degrees.
• Determine the length all the sides of the pattern blocks.
• Determine the circumfernce of the orange red circle.
• Determine the circumfernce of the green white circle.