Transformations and Constructions

Transformations: Core Concepts

• What are Transformations?

  • Transformations are movements of shapes in a plane. They change the position or size of a shape without altering its basic form.

• Types of Transformations:

  • Translation: Shifting a shape horizontally, vertically, or both.

    • Think of sliding a piece of paper across a desk.

  • Rotation: Turning a shape around a fixed point (the center of rotation).

    • Imagine spinning a wheel.

  • Reflection: Flipping a shape over a line (the line of reflection).

    • Like looking at your reflection in a mirror.

  • Dilation: Changing the size of a shape.

    • Enlargements or reductions.

• Key Concepts:

  • Congruence: Shapes that have the same size and shape are congruent. Translations, rotations, and reflections preserve congruence.

  • Similarity: Shapes that have the same shape but different sizes are similar. Dilations create similar shapes.

  • Coordinate Plane: Transformations can be described using coordinates on a coordinate plane.

Constructions: Core Concepts

• What are Constructions?

  • Constructions are precise drawings created using only a compass and straightedge (an unmarked ruler).

• Basic Constructions:

  • Bisecting a line segment: Dividing a line segment into two equal parts.

  • Constructing a perpendicular bisector: Finding the line that is perpendicular to a given line segment and passes through its midpoint.

  • Bisecting an angle: Dividing an angle into two equal angles.

  • Constructing a perpendicular line: Drawing a line perpendicular to a given line through a given point.

  • Constructing an equilateral triangle: Creating a triangle with all sides equal.

• Applications:

  • Constructions are used in various fields like architecture, engineering, and art. They help to create accurate and precise designs.