8th grade
geometry
STANDARDS
|
ESSENTIAL QUESTIONS
|
CC.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. 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. |
What is a transformation? What happenst to angles, lines, and line segments when they are transformed?
|
CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. 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.
|
What is a transformation? What happenst to angles, lines, and line segments when they are transformed?
|
CC.8.G.3 Understand congruence and similarity using physical models, transparencies, or geometry software. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
|
How is the coordinate system used to analyze transformations? How are congruence and similarity related to transformations?
|
CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. 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.
|
How can the use of transformations create two similar figures? How do ratios and similarity relate to dilations?
|
CC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. 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 three angles appear to form a line, and give an argument in terms of transversals why this is so.
|
How can you use knowledge of angle measurements to find unknown unknown angle measurments? How does knowing that two triangles are similar make it possible to solve mathematical problems.
|
CC.8.G.6 Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse.
|
How can the Pythagorean Theorem be used to solve problems? How can side lengths of a triangle be used to classify triangles?
|
CC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
|
How is the Pythagorean Theorem used in mathematical situations?
|
CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
|
How can you use the Pythagorean Theorem to determine the distance between two points?
|
CC.8.G.9 Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
|
What is the relationship between areal and volume? What is the relationship between volume and surface area?
|