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Edited 6/25/12 Beaverton School District Geometry Long-term and Supporting Learning Targets MA.HS.GE.ALT.01: I can demonstrate my understanding of the foundations of geometry. MA.HS.GE.AST.01.1: I can translate between vocabulary, symbols and/or a diagram to communicate. MA.HS.GE.AST.01.2: I can demonstrate my understanding of the undefined terms. MA.HS.GE.AST.01.3: I can use definitions, postulates, and theorems to build and defend a logical argument. MA.HS.GE.AST.01.4: I can apply inductive and deductive reasoning to build and defend a logical argument. MA.HS.GE.ALT.02: I can prove and apply congruence theorems dealing with angles and lines to solve problems and justify my solutions. MA.HS.GE.AST.02.1: I can apply and prove theorems and use properties dealing with vertical angles and a linear pair of angles. MA.HS.GE.AST.02.2: I can apply and prove theorems and use properties dealing with complementary and supplementary angles. MA.HS.GE.AST.02.3: I can apply and prove theorems and use properties dealing with parallel and perpendicular lines. MA.HS.GE.AST.02.4: I can use angle measures to prove that lines are parallel or perpendicular. MA.HS.GE.ALT.03: I can connect linear algebra and coordinates to geometric situations and use it to prove geometric theorems. (CCSS-G-GPE-4-7) MA.HS.GE.AST.03.1: I can use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle Prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2) MA.HS.GE.AST.03.2: I can prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. For example, find the equation of a line parallel or perpendicular to a given line that passes through a given point. 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 a point). Edited 6/25/12 Given a diagram, determine if two lines are parallel, perpendicular, or neither. MA.HS.GE.AST.03.3: I can find the point on a line segment between two given points that divides the segment in a given ratio (1/2, ¼, 1/8…). Use midpoint theorem. MA.HS.GE.AST.03.4: I can prove theorems about quadrilaterals (opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelograms with congruent diagonals. MA.HS.GE.ALT.04: I can prove and apply congruence theorems dealing with triangles to solve problems and justify my solutions. MA.HS.GE.AST.04.1: I can use a diagram that marks the congruent segments and angles and determine if two triangles are congruent. MA.HS.GE.AST.04.2: I can use a diagram that marks the congruent segments and angles and formally prove if two triangles are congruent. MA.HS.GE.AST.04.3: I can use Corresponding Parts of Congruent Triangles Theorem to determine and prove other statements. MA.HS.GE.AST.04.4: I can apply the congruence of polygons to solve problems. MA.HS.GE.ALT.05: I am able to use a variety of tools and methods to construct basic geometric figures. MA.HS.GE.AST.05.1: I can draw formal geometric constructions with a variety of tools and methods, which could include, but not limited to, the following; compass and straightedge, string, reflective devices, and dynamic geometric software. Formal Geometric Constructions should include: 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. MA.HS.GE.AST.05.2: I can apply and construct triangle properties including medians, centroids, circumcenters, orthocenters, and incenters. MA.HS.GE.AST.05.3: I can construct an equilateral triangle, a square and a regular hexagon inscribed in a circle. MA.HS.GE.AST.05.4: I can construct the inscribed and circumscribed circles of a triangle. MA.HS.GE.ALT.06: I can apply the laws of similarity to solve problems and prove my solutions MA.HS.GE.AST.06.1: I can apply the similarity of polygons to solve problems MA.HS.GE.AST.06.2: I can apply the triangle similarity theorems to solve problems, write and complete proofs. MA.HS.GE.AST.06.3: I can prove whether or not two shapes are similar. Edited 6/25/12 MA.HS.GE.ALT.07: I can solve for unknown lengths and angles in right triangles and justify my solutions. (CCSS-G-SRT-6-8) MA.HS.GE.AST.07.1: Given three side lengths, I can determine and justify whether a triangle can be created. MA.HS.GE.AST.07.2: I can use the Pythagorean Theorem to find unknown lengths of right triangles and determine if a triangle is right, obtuse, or acute. MA.HS.GE.AST.07.3: I can demonstrate and use properties of special right triangles. 30- 60-90 triangles 45-45-90 triangles MA.HS.GE.AST.07.4: I can use trigonometric ratios (sine, cosine and tangent) to find unknown lengths in right triangles. Explain and use the relationship between the sine and cosine of complementary angles. Understand that by similarity, side ratios in right triangles are properties of angles in the triangle, leading to definitions of trigonometric ratios for acute angles. MA.HS.GE.AST.07.5: I can use trigonometric ratios (sine, cosine, and tangent) to find the unknown angles in right triangles. Explain and know the differences between; sin, sin-1 , cos, cos-1 , tan, tan-1 and when to use them. MA.HS.GE.AST.07.6: In applied problems I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles. MA.HS.GE.ALT.08: I can prove theorems and utilize the properties to solve problems of two-dimensional polygons, including real-world applications. (CCSS-G-CO-10-11, CCSS-G-MG-1-3) MA.HS.GE.AST.08.1: I can classify polygons based on characteristics. Triangle classifications: right, acute, obtuse, scalene, equilateral, isosceles. Quadrilateral classifications: trapezoid, rectangle, square, kite, parallelogram, and rhombus. General classifications: by number of sides, by properties of quadrilaterals, equilateral, equiangular, regular, convex, concave. MA.HS.GE.AST.08.2: I can find the perimeter and area of a variety of polygons, including applications. Including: regular polygons, quadrilaterals, triangles, composite shapes, and shaded regions. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g. using the distance formula) Apply concepts of density based on area and volume in modeling situations (ex: person per square mile) MA.HS.GE.AST.08.3: I can find the unknown sides and angles of a variety of polygons, including applications. Given area or perimeter of a polygon, find a missing dimension. Given a diagram or information, find a missing angle. Edited 6/25/12 MA.HS.GE.AST.08.4: Given similar figures, I can compare and compute their respective areas and volumes. *Can be taught in 2-D and 3-D. MA.HS.GE.ALT.09: I can apply properties of circles to solve problems and justify my solutions. (CCSS-G-C-1-5) MA.HS.GE.AST.09.1: I can apply properties of angles formed by chords, tangents and secants to solve problems. This includes the use of congruent circles, concentric circles, radius, chord, diameter, tangent, point of tangency, central angle, inscribed angle. MA.HS.GE.AST.09.2: I can prove that all circles are similar. MA.HS.GE.AST.09.3: I can state and use precise definitions of circles, arcs, degrees, radians, arc measure, arc length, and areas of sectors. MA.HS.GE.AST.09.4: I can derive the formula for the area of a sector of a circle. MA.HS.GE.AST.09.5: I can give an informal argument for the circumference of a circle, and for the area of a circle. MA.HS.GE.AST.09.6: I can use coordinates to prove that a point lies on a circle and circumscribed and inscribed circles. MA.HS.GE.AST.09.7: I can prove properties of angles for a quadrilateral inscribed in a circle. MA.HS.GE.ALT.10: I can apply the characteristics and properties of ThreeDimensional figures to solve problems, including applications and justify my solutions. (CCSS-G-GMD-1-3, CCSS-G-MG-1-3) MA.HS.GE.AST.10.1: I can identify and classify 3-D figures from a model, a net, and different perspectives. Recognize face, vertex, edge, diagonal, lateral face, base, altitude. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder) MA.HS.GE.AST.10.2: I can find the surface area of 3-Dimensional figures including applications. Given the surface area of 3-Dimensional figures, I can find missing measures. Applications situations should specifically address concepts of density and optimization as well as other situations. MA.HS.GE.AST.10.3: I can find the volume of 3-Dimensional figures, including applications. Give an informal argument for the volume of a cylinder, pyramid and cone. Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. Given the volume area of 3-Dimensional figures, I can find missing measures. 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) MA.HS.GE.AST.10.4: I can visualize relationships between 2-D and 3-D figures. Identify the shapes of 2-dimensional cross-sections of 3-dimensional objects, and identify 3-dimensional objects generated by rotations of 2-dimensional objects. Edited 6/25/12 MA.HS.GE.ALT.12: I can use independence and conditional probability formally to interpret data and compute the probabilities of compound events. (CCSS-S-CP-1-7) MA.HS.GE.AST.12.1: I can describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”). MA.HS.GE.AST.12.2: I can demonstrate that two events A and B are independent of the probability of A and B occurring together is the products of their probabilities, and use this characterization to determine if they are independent. MA.HS.GE.AST.12.3: I can use the general formula to compute the conditional probability of A given B as P(A and B)/P(B). MA.HS.GE.AST.12.4: I can use a two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. MA.HS.GE.AST.12.5: I can recognize and explain the concepts of conditional probability and independent in every day language and every day situations. MA.HS.GE.AST.12.6: I can model conditional probability of an event through Venn Diagrams and Factor Trees. MA.HS.GE.AST.12.7: I can apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. Due to a reduction to the number of student contact days for 2012-13, it is recommended that this target be included only if time allows or it is naturally integrated with another target or targets. MA.HS.GE.ALT 11: I can apply and analyze transformations of figures. (CCSS-G-CO-25) MA.HS.GE.AST.11.1: I can identify lines of symmetry and distinguish between rotation and reflection symmetries given a rectangle, parallelogram, trapezoid, or regular polygon, MA.HS.GE.AST.11.2: I can identify and draw rigid transformations of 2dimensional figures on and off the coordinate plane. Transformations should include translations, reflections across either axis, or y = +/- x, and rotations about the origin in multiples of 90 degrees. Students can use graph paper, tracing paper, or geometry software to represent rigid transformations. MA.HS.GE.AST.11.3: I can identify and apply non-rigid transformations of geometric figures on and off the coordinate plane. Transformations should address scale factor, dilations including origin centered dilations, and similarity.