Louisiana Administrative Code
Title 28 - EDUCATION
Part CLXXI - Bulletin 745-Louisiana Teaching Authorizations of School Personnel
Chapter 19 - Grade 8
Section CLXXI-1907 - Geometry

A. Verify experimentally the properties of rotations, reflections, and translations.

B. Explain 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. (Rotations are only about the origin and reflections are only over the y-axis and x-axis in grade 8.)

C. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in grade 8.)

D. Explain 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. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in grade 8.)

E. 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.

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.

F. Explain a proof of the Pythagorean Theorem and its converse using the area of squares.

G. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

H. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

I. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.