Administrative Rules of Montana › Department 10 - EDUCATION › Chapter 10.53 - CONTENT STANDARDS › Subchapter 10.53.5 - Mathematics Content Standards › Rule 10.53.516 - MONTANA HIGH SCHOOL MATHEMATICS GEOMETRY CONTENT STANDARDS

Current through Register Vol. 13, July 5, 2024
(1) Mathematics geometry: congruence content
				standards for high school are:
(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 transparencies and geometry software; describe transformations as
				functions that take points in the plane as inputs and give other points as
				outputs; and 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 and 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 and 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 theorems about lines and angles;
				theorems include: vertical angles are congruent, when a transversal crosses
				parallel lines, alternate interior angles are congruent, corresponding angles
				are congruent, and points on a perpendicular bisector of a line segment are
				exactly those equidistant from the segment's endpoints;
(j) prove theorems about triangles; theorems
				include: measures of interior angles of a triangle sum to 180°, 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, and the
				medians of a triangle meet at a point;
(k) prove 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,
				including those representing Montana American Indians, with a variety of tools
				and methods (compass and straightedge, string, reflective devices, paper
				folding, dynamic geometric software, etc.); 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; and
(m) construct an equilateral triangle, a
				square, and a regular hexagon inscribed in a circle.