TCS - Transformations, Congruence, and Similarity Module Overview
Transformations, Congruence, and Similarity Module Overview
Introduction
You've heard the words flip, slide, turn, and enlarge since you can remember, right? You know from personal experience that if you put a piece of paper on the table and slide it down the table two feet, that it doesn't lose its properties of perimeter, area, etc. In mathematics, we call these transformations. The transformations we'll be learning about are reflections
, translations
Essential Questions
- How can we show that a two-dimensional figure is congruent to another if the second is a sequence of rotations, reflections, or translations?
- What are the effects of dilations, translations, rotations, and reflections on the coordinates of two dimensional figures?
- How can we show that a two-dimensional figure is similar to another if the second is a sequence of rotations, reflections, translations, or dilations?
- What angle relationships can we draw from parallel lines being cut by a transversal?
- What is the sum of the angles of a triangle?
- How can we determine the similarity of triangles based on the angle measures of the triangle?
Key Terms
The following key terms will help you understand the content in this module.
Congruent Figures - Figures that have exactly the same size, shape, and measurements.
Similar Figures - Figures that have the same shape, but not the same size and are proportional to one another.
Transformation - A change. In mathematics, this change can be described as a mapping between two sets of points.
Reflection - A transformation that flips the image creating its mirror image.
Rotation- A transformation that turns an image about a given point.
Center of Rotation - The point about which a figure is rotated.
Angle of Rotation - The number of degrees a figure is rotated.
Translation - A transformation that slides a figure in a straight line in which no flips or turns are made.
Dilation - A transformation that makes an object larger or smaller by a scale factor of the original.
Preimage - The original figure, before a transformation occurs.
Image - The new figure resulting from a transformation.
Scale Factor - The constant by which a figure is increased or decreased when dilated.
Parallel Lines - Two or more lines that lie in the same plane and never intersect.
Transversal - A line that intersects two other lines.
Corresponding Angles - Angles that are in the same place with respect to the transversal but on different lines.
Alternate Interior Angles - Angles that are on the interior of parallel lines, but on opposite sides of the transversal.
Alternate Exterior Angles - Angles that are on the exterior of the parallel lines and on opposite sides of the transversal.
Same side interior angles - Angles that are on the same side of the transversal and on the interior of the parallel lines.
Adjacent Angles - Angles that are beside each other; they share a common side and a common vertex.
Vertical Angles - A pair of angles with a common vertex whose sides form opposite rays. They are sometimes referred to as opposite angles.
Triangle Sum Theorem - The theorem that states that all the angles in a triangle will always add to 180 degrees.
Exterior Angle Theorem - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Angle - Angle Postulate for Similar Triangles - States that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.
IMAGE SOURCE: CLIPART