Common Core Learning Standards Concepts Embedded Skills Vocabulary Understand congruence and similarity using physical models, transparencies, or geometry software. Transformations Translate, rotate, and reflect parallel lines on a coordinate plane. Parallel lines Rotation Reflection Translation Transformation Slope/rate of change Corresponding parts Explain that the slope and distance between two parallel lines will be preserved after a translation, rotation, or reflection of the parallel lines. 8.G.1. Verify experimentally the properties of rotations, reflections, and translations: 8.G.1c. Parallel lines are taken to parallel lines. Identify corresponding lines after a translation, rotation, or reflection, by using prime notation. Show that parallel lines are translated, rotated, or reflected parallel lines. SAMPLE TASKS
Common Core Learning Standards Concepts Embedded Skills Vocabulary Understand congruence and similarity using physical models, transparencies, or geometry software. Congruent figures Explain the preservation of congruence when a figure is rotated, reflected, and/or translated. Transformation Reflection Rotation Translation Congruence Corresponding parts sequence Describe the sequence of transformations that occurred from the original 2D figure to the image. 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. Draw a reflection of an object. Draw a translation of an object. Draw a rotation of an object. Name corresponding parts in congruent figures. SAMPLE TASKS Figure 1 is transformed using two steps to form figure 2, as shown on this coordinate plane. Part A: Complete the statements below to show which corresponding sides in each figure are congruent. Part B: Describe the two steps used to complete this transformation. Step 1: _________________________________________________________________ Step 2: _________________________________________________________________
Common Core Learning Standards Concepts Embedded Skills Vocabulary Understand congruence and similarity using physical models, transparencies, or geometry software. Prove/explain why the three angles of a triangle equal 180°. Triangle Similar Parallel lines Transversal Congruent Supplementary Linear pair Corresponding Vertical Alternate, exterior, interior angles Prove/explain why the exterior angle theorem of a triangle. 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. Prove/explain why alternate interior angles are congruent. Prove/explain why alternate exterior angles are congruent. Prove/explain why corresponding angles are congruent. Prove/explain why angle-angle criterion works to prove similarity of two triangles. SAMPLE TASKS Given that is parallel to , prove that the angles of triangle BED add up to .
Common Core Learning Standards Concepts Embedded Skills Vocabulary Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Write and solve using the formula for the volume of a cone. Volume Cone Cylinder Sphere Area Base Write and solve using the formula for the volume of a cylinder. 8.G.9. Know the formulas for the volumes of cones, Write and solve using the formula for the volume of a sphere.