Illuminations: Cutting Corners

# Cutting Corners

This tool provides an excellent opportunity for students to talk about the names and attributes of shapes they do not regularly meet. For example, they will most likely encounter scalene triangles, with no congruent sides; isosceles triangles, with at least two congruent sides; and equilateral triangles, which are special isosceles triangles that have three congruent sides. When appropriate, point out to the students that rectangles are special parallelograms that have right angles, rhombuses are special parallelograms that have four equal sides, and squares are special rhombuses with four equal angles as well as four equal sides.

Young students have difficulty recognizing shapes that have been rotated or flipped. In Cutting Corners, students have opportunities to create and view shapes in different orientations.

### Instructions

The slide, turn, flip, and delete buttons can be used on any shape.

 Slide Rotate Flip Delete

Click on the button and then on the shape or the cut line. The rotate button turns a shape 30° clockwise, or one-twelth of a complete rotation. The Flip button flips a shape over a horizontal line.

To turn off a button, either click on another button or click on the active button a second time.

### Exploration

Can you cut a rectangle to get two smaller rectangles whose shape and size are the same? (There are two different ways to do this.)

Try to answer the following questions using this tool.

 Can you cut a… to make… triangle one triangle and one trapezoid? two triangles? one triangle and one quadrilateral (that is not a trapezoid)? rectangle one triangle and one pentagon? two trapezoids? two rectangles of different shapes and sizes? two triangles? a triangle and a trapezoid? trapezoid one triangle and one trapezoid? one triangle and one parallelogram? two trapezoids? two triangles? one triangle and one quadrilaterial? one triangle and one pentagon?

### NCTM Resources

 More and Better Mathematics for All Students
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