Embed Size (px)
Citation preview
Unit 9: TransformationsScale for Unit 9
4Through independent work beyond what was taught in class, students could (examples include, but are not limited to): - Design and create a puzzle that requires a combination of isometries to solve. - Create a new logo for a business by tessellating its current logo.
3
The students will: - Represent transformations in the plane.- 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 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry a figure onto itself. - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. - Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. - Specify a sequence of transformations that will carry a given figure onto another- 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. - 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- Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions. - Verify experimentally the properties of dilations given by a center and a scale factor:
o 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. o The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
2
The students will:- Determine the meaning of symbols, key terms, and other geometry specific words and phrases. - Identify transformations in the coordinate plane, rotations and reflections that carry a figure onto itself, and congruent figures.- Classify rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. - Name the transformation used when given a pre-image and an image. - Recognize rigid motions. - Recall the definition triangle congruence, how to prove congruence in triangles, the properties of dilations, and the definition similarity in geometric figures.- Identify scale factor.
1 The student will be able to correctly use the following vocabulary: transformation, reflection, rotation, dilation, and scale factor.
BELLWORK:
Date: __________________________ Date: __________________________
Page 1 of 21
BELLWORK:
Date: __________________________ Date: __________________________
Date: __________________________ Date: __________________________
Page 2 of 21
Section 9-1 – TranslationsVocabulary Word Definition Picture
Transformation
Pre-Image and Image
Isometry
Translation
Composition of Transformations
Reflection and Line of
Reflection
Rotation
Symmetry
Dilation
Page 3 of 21
Page 4 of 21
Section 9-2 – Reflections
Page 5 of 21
Section 9-3 – Rotations
Page 6 of 21
Page 7 of 21
Section 9-4 – Symmetry
Page 8 of 21
Page 9 of 21
MIDUNIT REVIEW
Page 10 of 21
Page 11 of 21
Section 9-5 – Dilations
Page 12 of 21
Section 9-6 – Compositions of Reflections
Page 13 of 21
Page 14 of 21
Section 9-7 – Tessellations
A _______________________, or ________________, is a repeating pattern of figures that completely covers a _______________, without
gaps or overlaps. _____________________ can be made using __________________, __________________, and _____________________.
Page 15 of 21
Could you make a tessellation with the following shapes?
A. A Regular Hexagon
B. A 13-gon
TESSELATIONS ACTIVITY:
Page 16 of 21
Page 17 of 21
Page 18 of 21
UNIT 9 REVIEW:
Page 19 of 21
Page 20 of 21
Page 21 of 21
