Geometry Strategies

MAGS: Geometry Strategies

MAGS.A: Geometry

MAGS.B: Statistics and Probability

MAGS.A.3: know and apply the 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

MAGS.A.4: describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates

MAGS.A.10: 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

MAGS.A.11: explain how the criteria for triangle congruence (i.e., ASA, SAS, SSS, HL, AAS) follow from the definition of congruence in terms of rigid motions

MAGS.A.12: use informal arguments to establish facts about the angle sum and exterior angles of triangles and about the angles created when parallel lines are cut by a transversal

MAGS.A.13: prove theorems about lines and angles (i.e., 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 segment's endpoints)

MAGS.A.15: informally prove the Pythagorean Theorem and its converse geometrically (i.e., using area model)

MAGS.A.16: prove theorems about triangles (i.e., 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)

MAGS.A.17: prove theorems about parallelograms (i.e., opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals)

MAGS.A.18: use congruence criteria for triangles to solve problems and to prove relationships in geometric figures

MAGS.A.22: prove theorems about triangles (i.e., a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem using triangle similarity)

MAGS.A.23: use similarity criteria for triangles to solve problems and to prove relationships in geometric figures

MAGS.A.24: understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles

MAGS.A.25: explain and use the relationship between the sine and cosine of complementary angles

MAGS.A.26: use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

MAGS.A.27: prove that all circles are similar (i.e., using transformations; ratio of circumference to the diameter is a constant)

MAGS.A.35: use volume formulas for cylinders, pyramids, cones, and spheres to solve problems

MAGS.A.38: prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point)

MAGS.A.40: use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula)

MAGS.A.43: use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder)

MAGS.A.44: apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot)

MAGS.A.45: apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)

MAGS.B.49: construct and interpret two-way frequency tables of data when two categories are associated with each object being classified; use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities (e.g., collect data from a random sample of students in your school on their favorite subject among math, science, and English; estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade; do the same for other subjects and compare the results)

MAGS.B.51: find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in context

MAGS.B.52: apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in context