La. Admin. Code tit. 28 § CLXXI-1907

Current through Register Vol. 50, No. 9, September 20, 2024

Section CLXXI-1907 - Geometry

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

1. Lines are taken to lines, and line segments to line segments of the same length.

2. Angles are taken to angles of the same measure.

3. Parallel lines are taken to parallel lines.

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.

La. Admin. Code tit. 28, § CLXXI-1907

Promulgated by the Board of Elementary and Secondary Education, LR 421056 (7/1/2016).

AUTHORITY NOTE: Promulgated in accordance with R.S. 17.6, R.S. 17:24.4, and R.S. 17:154.