Bellringer 9 3 1 Reflections MAFS 912 GCO

Bellringer #9

3 -1: Reflections MAFS. 912. G-CO. 1. 2 Represent transformations in the plane using, e. g. , transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS. 912. G-CO. 1. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MAFS. 912. G-CO. 1. 5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e. g. , graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Rigid Motion • A rigid motion is a transformation that preserves length and angle measure. • Are the transformations a rigid motion? Explain.

Quadrilateral FGHJ has coordinates �� (�� , �� ), �� (−�� , �� ) • When any point �� (�� , �� ) on the coordinate plane is reflected across the x-axis, its image is �� ′(�� , −�� ). • Graph and label FGHJ and the Reflection across the x-axis. • When any point �� (�� , �� ) on the coordinate plane is reflected across the y-axis, its image is �� ′(−�� , �� ). • Graph and label FGHJ and the Reflection across the y-axis.

What are the coordinates of ���� (△������ )where t is the  line �� =�� ?

Bellringer #10

3 -2: Translations MAFS. 912. G-CO. 1. 2 Represent transformations in the plane using, e. g. , transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS. 912. G-CO. 1. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MAFS. 912. G-CO. 1. 5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e. g. , graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

What translation rule maps ���� onto �� ′�� ′?

A mover moved a box from A to B to C. What single transformation describes the move from A to C?

Bellringer #11

3 -3: Rotations MAFS. 912. G-CO. 1. 2 Represent transformations in the plane using, e. g. , transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. MAFS. 912. G-CO. 1. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MAFS. 912. G-CO. 1. 5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e. g. , graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. MAFS. 912. G-CO. 2. 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.

Bellringer #12 • Rotate and draw PQRS 90° counterclockwise about the origin if the vertices are P(1, − 2), Q(0, 2), R(3, 2), S(3, − 3).

3 -4: Compositions of Isometries MAFS. 912. G-CO. 1. 5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e. g. , graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. MAFS. 912. G-CO. 2. 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.

Is there a rigid motion that maps △������ to △�� ′�� ′?

What glide reflection maps △������ to △�� ″�� ″?

What is the glide reflection that maps △������ to △�� ″�� ″?

Bellringer #13

7 -1: Dilations MAFS. 912. G-CO. 1. 2 Represent transformations in the plane using, e. g. , transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not MAFS. 912. G-CO. 1. 5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e. g. , graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another MAFS. 912. G-SRT. 1. 1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Rectangle �� ′�� ′ is a dilation with center P of ABCD. How are the side lengths and angle measures of ABCD related to those of �� ′�� ′?

Quadrilateral �� ′�� ′ is a dilation of JKLM. What is the scale factor?

What are the vertices of ���� (△����� )?

7 -2: Similarity Transformations MAFS. 912. G-SRT. 1. 1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. MAFS. 912. G-SRT. 1. 2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides MAFS. 912. G-C. 1. 1 Prove that all circles are similar.

Compositions with Similarity If line m is represented by the equation �� = −�� , what is a graph of the image (����∘����. �� ) (△������ )?