Louisiana Administrative Code › Title 28 - EDUCATION › Part CLXXI - Bulletin 745-Louisiana Teaching Authorizations of School Personnel › Chapter 25 - Geometry › Section CLXXI-2501 - Geometry

Current through Register Vol. 50, No. 6, June 20, 2024
A. Know precise
				definitions of angle, circle, perpendicular line, parallel line, and line
				segment, based on the undefined notions of point, line, distance along a line,
				and distance around a circular arc.
B. Represent transformations in the plane
				using, e.g., transparencies, tracing paper, or geometry software; describe
				transformations as functions that take points in the plane as inputs and give
				other points as outputs. Compare transformations that preserve distance and
				angle to those that do not (e.g., translation versus horizontal stretch).
C. Given a rectangle,
				parallelogram, trapezoid, or regular polygon, describe the rotations and
				reflections that carry it onto itself.
D. Develop definitions of rotations,
				reflections, and translations in terms of angles, circles, perpendicular lines,
				parallel lines, and line segments.
E. Given a geometric figure and a rotation,
				reflection, or translation, draw the transformed figure using, e.g., graph
				paper, tracing paper, or geometry software. Specify a sequence of
				transformations that will carry a given figure onto another.
F. Use geometric descriptions of rigid
				motions to transform figures and to predict the effect of a given rigid motion
				on a given figure; given two figures, use the definition of congruence in terms
				of rigid motions to decide if they are congruent.
G. Use the definition of congruence in terms
				of rigid motions to show that two triangles are congruent if and only if
				corresponding pairs of sides and corresponding pairs of angles are
				congruent.
H. Explain how the
				criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition
				of congruence in terms of rigid motions.
I. Prove and apply theorems about lines and
				angles. (Theorems include: vertical angles are congruent; when a transversal
				crosses parallel lines, alternate interior angles are congruent and
				corresponding angles are congruent; points on a perpendicular bisector of a
				line segment are exactly those equidistant from the segments
				endpoints.)
J. Prove and apply
				theorems about triangles. (Theorems include: measures of interior angles of a
				triangle sum to 180 degrees; base angles of isosceles triangles are congruent;
				the segment joining midpoints of two sides of a triangle is parallel to the
				third side and half the length; the medians of a triangle meet at a
				point.)
K. Prove and apply theorems
				about parallelograms. (Theorems include: opposite sides are congruent, opposite
				angles are congruent, the diagonals of a parallelogram bisect each other, and
				conversely, rectangles are parallelograms with congruent diagonals.)
L. Make formal geometric constructions with a
				variety of tools and methods, e.g., compass and straightedge, string,
				reflective devices, paper folding, or dynamic geometric software.
Examples: Copying a segment; copying an angle; bisecting a
				  segment; bisecting an angle; constructing perpendicular lines, including the
				  perpendicular bisector of a line segment; and constructing a line parallel to a
				  given line through a point not on the line.
M. Construct an equilateral triangle, a
				square, and a regular hexagon inscribed in a circle.
N. Verify experimentally the properties of
				dilations given by a center and a scale factor.
1. A dilation takes a line not passing
				through the center of the dilation to a parallel line, and leaves a line
				passing through the center unchanged.
2. The dilation of a line segment is longer
				or shorter in the ratio given by the scale factor.