Congruency Similarity and Transformations Congruent Objects are congruent

Congruency, Similarity, and Transformations

Congruent Objects are congruent if they are exactly the same shape and size.

Are these shapes congruent?

Similar objects are the same shape but are not the same size.

Are these shapes similar?

Corresponding Parts Matching parts of congruent or similar figures.

What parts are corresponding? A B C D E F G H B X Z A C Y

Vocabulary Ø Transformation Ø Image Ø Translation Ø Reflection Ø Rotation

Vocabulary • Transformation is an operation that maps an original geometric figure (called a preimage), onto a new figure (called the image). • A congruence transformation (also called a rigid transformation or an isometry) is a transformation that creates an image that is congruent to the preimage • Reflection • Translation • Rotation

Terms Image: The new figure created from the transformation Ø Translation (slide ): Moves every point of a ( figure the same distance in the same direction Ø Reflection (flip ( ): A line of reflection is used and creates a mirror image of the figure Ø Rotation (turn ): turns a figure about a fixed ( point (center of rotation) Ø

Transformations A change in position of a figure. Ø Translation Ø Reflection Ø Rotation Let’s see these transformations in action!

Translation (Slide) A figure moves along a straight line. Figure 1 Figure 2

Identify Congruence Transformations A. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its image are in the same position, just 5 units right and 2 units down. Answer: This is a translation.

Reflection (Flip) A mirror image is created across a line. Figure 1 Figure 2

Identify Congruence Transformations C. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its image are the same distance from the x-axis. Answer: This is a reflection.

Rotation (Turn) A figure turns around a point. 90° 180° Figure 2 Figure 1 180° Figure 1 Figure 2

Identify Congruence Transformations B. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its image are the same distance from the origin. The angles formed by each pair of corresponding points and the origin are congruent. Answer: This is a rotation.

Name the Transformation 1 Rotation 1 Translation 2 2 1 Rotation 180° 1 2 2 Reflection 90°

Example 1 A. Identify the type of congruence transformation shown as a reflection, translation, or rotation. A. reflection B. translation C. rotation D. none of these

Example 2 B. Identify the type of congruence transformation shown as a reflection, translation, or rotation. A. reflection B. translation C. rotation D. none of these

Example 3 C. Identify the type of congruence transformation shown as a reflection, translation, or rotation. A. reflection B. translation C. rotation D. none of these