Exploring 2-D Shapes and Transformations

The properties of a triangle change based on its orientation.

Triangles can only exist in one specific orientation.

The angles of a triangle vary with its position in space.

The properties of a triangle remain consistent regardless of its orientation.

A square with points A, B, C, D; lines AB, BC, CD, DA; and angles A, B, C, D (all 90 degrees).

A triangle with points A, B, C; lines AB, BC, CA; and angles A, B, C (varying degrees).

A rectangle with points A, B, C, D; lines AB, BC, CD, DA; and angles A, B, C, D (all 90 degrees).

A rectangle with points A, B, C, D; lines AB, AC, CD, DA; and angles A, B, C, D (varying degrees).

Rectangle

Circle

Triangle

Square

The line of symmetry is the axis along which a shape can be folded to create two identical halves.

The line of symmetry is the perimeter of the shape.

The line of symmetry is the longest side of the shape.

The line of symmetry is the center point of the shape.

A circle with no lines of symmetry.

A square with four lines of symmetry: two diagonals and two bisecting lines.

A rectangle with only one line of symmetry: the vertical bisector.

A triangle with three lines of symmetry: one vertical and two horizontal.

The shape is rotated 90 degrees.

The shape is flipped vertically.

The shape is stretched horizontally.

The shape is translated to a new position.

The shape is rotated 90 degrees clockwise around the center.

The shape is stretched vertically by 90 degrees.

The shape is rotated 90 degrees counterclockwise.

The shape is flipped upside down.

(6, 2)

(6, 4)

(5, 3)

(2, 2)

A circle with one line of symmetry.

A triangle with three lines of symmetry.

A rectangle with two lines of symmetry.

A square with four lines of symmetry.

Rotating a triangle 90 degrees results in new vertices A'(2, -1), B'(4, -3), and C'(2, -5).

Translating a triangle 3 units to the right results in new vertices A'(4, 2), B'(6, 4), and C'(4, 2).

Scaling a triangle by a factor of 2 results in new vertices A'(2, 4), B'(6, 8), and C'(10, 4).

Reflecting a triangle over the y-axis results in new vertices A'(-1, 2), B'(-3, 4), and C'(-5, 2).