8G-Understand+congruence+and+similarity+using+physical+models,+transparencies,+or+geometry+software

8.G.1.Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. //For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.// || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === G.1 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. G.2 2. Reason abstractly and quantitatively. 4. Model with mathematics. 6. Attend to precision. 7. Look for and make use of structure. G.3 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. <span style="font-family: Arial,Helvetica,sans-serif;">6. Attend to precision. <span style="font-family: Arial,Helvetica,sans-serif;">7. Look for and make use of structure. <span style="font-family: Arial,Helvetica,sans-serif;">G.4 <span style="font-family: Arial,Helvetica,sans-serif;">2. Reason abstractly and quantitatively. <span style="font-family: Arial,Helvetica,sans-serif;">4. Model with mathematics. <span style="font-family: Arial,Helvetica,sans-serif;">5. Use appropriate tools strategically. <span style="font-family: Arial,Helvetica,sans-serif;">6. Attend to precision. <span style="font-family: Arial,Helvetica,sans-serif;">7. Look for and make use of structure. <span style="font-family: Arial,Helvetica,sans-serif;">G.5 <span style="font-family: Arial,Helvetica,sans-serif;">3. Construct viable arguments and critique the reasoning of others. <span style="font-family: Arial,Helvetica,sans-serif;">4. Model with mathematics. <span style="font-family: Arial,Helvetica,sans-serif;">5. Use appropriate tools strategically. <span style="font-family: Arial,Helvetica,sans-serif;">6. Attend to precision. <span style="font-family: Arial,Helvetica,sans-serif;">7. Look for and make use of structure. || 8.TT.1 Use technology and other resources for assigned tasks. 8.SE.1 Analyze responsible behaviors when using information and technology resources. 8.SI.1 Evaluate information resources based on specified criteria. 8.TT.1 Use technology and other resources for assigned tasks. || ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking** Remembering Understanding Applying Analyzing Evaluating Creating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**=== reflections and rotations. Characteristics of figures, such as lengths of line segments, angle measures and parallel lines, are explored before the transformation (pre-image) and after the transformation (image). Students understand that these transformations produce images of exactly the same size and shape as the pre-image and are known as rigid transformations. Translations, reflections and rotations are examples of rigid transformations. A rigid transformation is one in which the pre-image and the image both have exactly the same size and shape since the measures of the corresponding angles and corresponding line segments remain equal (are congruent). Students examine two figures to determine congruency by identifying the rigid transformation(s) that produced the figures. Students recognize the symbol for congruency and write statements of congruency. clockwise and counterclockwise), recognizing the relationship between the coordinates and the transformation. Students recognize the relationship between the coordinates of the pre-image, the image and the scale factor for a dilation from the origin. Using the coordinates, students are able to identify the scale factor (image/pre-image). Students identify the transformation based on given coordinates. congruent angles and sides that are proportional. Similar figures are produced from dilations. Students describe the sequence that would produce similar figures, including the scale factors. Students understand that a scale factor greater than one will produce an enlargement in the figure, while a scale factor less than one will produce a reduction in size. a) angle sums and exterior angle sums of triangles, b) angles created when parallel lines are cut by a transversal, and c) the angle-angle criterion for similarity of triangle. Students construct various triangles and find the measures of the interior and exterior angles. Students make conjectures about the relationship between the measure of an exterior angle and the other two angles of a triangle. (the measure of an exterior angle of a triangle is equal to the sum of the measures of the other two interior angles) and the sum of the exterior angles (360º). Using these relationships, students use deductive reasoning to find the measure of missing angles. Students construct parallel lines and a transversal to examine the relationships between the created angles. Students recognize vertical angles, adjacent angles and supplementary angles from 7th grade and build on these relationships to identify other pairs of congruent angles. Using these relationships, students use deductive reasoning to find the measure of missing angles. Students can informally conclude that the sum of the angles in a triangle is 180º (the angle-sum theorem) by applying their understanding of lines and alternate interior angles. Students construct various triangles having line segments of different lengths but with two corresponding congruent angles. Comparing ratios of sides will produce a constant scale factor, meaning the triangles are similar. Students solve problems with similar triangles.
 * ===**Common Core Standards**===
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 8.G.1** Students use compasses, protractors and rulers or technology to explore figures created from translations,
 * 8.G.2** This standard is the students’ introduction to congruency. Congruent figures have the same shape and size.
 * 8.G.3** Students identify resulting coordinates from translations, reflections, and rotations (90º, 180º, and 270º both
 * 8.G.4** Similar figures and similarity are first introduced in the 8th grade. Students understand similar figures have
 * 8.G.5** Students use exploration and deductive reasoning to determine relationships that exist between the following:

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**
I can understand congruence and similarity using physical models, transparencies, or geometry software. I can determine the length of lines and angles after a translation. I can determine the length of lines and angles after a reflection. I can determine the length of lines and angles after a rotation. I can demonstrate that congruent figures have the same shape and size even after a rotation, reflection or translation. I can describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. I can demonstrate that similar figures have angles with the same measure and sides that are proportional. I can describe a sequence of events that goes from the pre-image to image. I can determine relationships between angle sums and exterior angle sums of triangles. I can determine relationships between angles created when parallel lines are cut by a tranversal. I can determine relationships between the angle- angle criterion for similarity of triangle.
 * 8.G.1**
 * 8.G.2**
 * 8.G.3**
 * 8.G.4**
 * 8.G.5**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
translations, rotations, reflections, line of reflection, center of rotation, clockwise, counterclockwise, parallel lines, betweenness, congruence, congruent symbol, reading A’ as “A prime”, similarity, dilations, pre-image, image, rigid transformations, exterior angles, interior angles, alternate interior angles, angle-angle criterion, deductive reasoning, vertical angles, adjacent, supplementary, complementary, corresponding, scale factor, transversal, parallel

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Hands-on activities book pages 201-223

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
Navigating through Geometry chapter 3

[[file:fun_websites_for_8th_grade_math.doc]]
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== Carnegie Learning chapters 7, 8, 9, and 10 Mathematics stations pages 124, 133, 140, and 147
 * Quantile G.1a**
 * Quantile G.1b**
 * Quantile G.1c**
 * Quantile G.2**
 * Quantile G.3**
 * Quantile G.4**
 * Quantile G.5**

media type="custom" key="19629164"
media type="custom" key="19629462" NYC Common core aligned task and assessment

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===
 * Refer to NC DPI unpacked content pages 26-32**
 * Refer to Arizona Academic Content standards pages 18-23**