Key Concept: Reflections, Translations, and Rotations CCSS Now New Vocabulary Key Concept: Reflections, Translations, and Rotations Example 1: Identify Congruence Transformations Example 2: Real-World Example: Identify a Real-World Transformation Example 3: Verify Congruence after a Transformation Lesson Menu

Mathematical Practices Content Standards G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Mathematical Practices 1 Make sense of problems and persevere in solving them. 7 Look for and make use of structure. CCSS

SWBAT use mathematical vocabulary (key terms in geometry) IOT describe transformations in the coordinate plane. SWBAT graph pre-images and images under reflection and rotation using a variety of tools IOT analyze the properties of transformations. Then/Now

congruence transformation isometry reflection translation rotation preimage image congruence transformation isometry reflection translation rotation Vocabulary

Concept

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: Example 1

Answer: This is a translation. 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. Example 1

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: Example 1

Answer: This is a rotation. 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. Example 1

Each vertex and its image are the same distance from the x-axis. 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: Example 1

Each vertex and its image are the same distance from the x-axis. 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. Example 1

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

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

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

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

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

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

Identify a Real-World Transformation BRIDGES Identify the type of congruence transformation shown by the image of the bridge in the river as a reflection, translation, or rotation. Answer: Example 2

Identify a Real-World Transformation BRIDGES Identify the type of congruence transformation shown by the image of the bridge in the river as a reflection, translation, or rotation. Answer: The image is a reflection, with the line at which the bridge meets the water as the line of reflection. Example 2

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

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

Verify Congruence after a Transformation Triangle PQR with vertices P(4, 2), Q(3, –3), and R(5, –2) is a transformation of ΔJKL with vertices J(–2, 0), K(–3, –5), and L(–1, –4). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. Understand You are asked to identify the type of transformation—reflection, translation, or rotation. Then, you need to show that the two figures are congruent. Plan Use the Distance Formula to find the measure of each side. Then show that the two triangles are congruent by SSS. Example 3

Verify Congruence after a Transformation Solve Graph each figure. The transformation appears to be a translation 6 units right and 2 units up. Find the measures of the sides of each triangle. Example 3

Verify Congruence after a Transformation Example 3

Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. A. B. C. D. Example 3

Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. A. B. C. D. Example 3