**2013 Geometry Learning Targets**

Some things we will always be working on
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1. I can use measures and properties of geometric shapes to describe real world objects.
2. I can classify and describe a real world object as a known geometric object – use this to solve problems in context.
3. I can focus on situations well modeled by trigonometric ratios for acute angles.
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1. I can define density.
2. I can apply concepts of density based on area and volume to model real-life situations (e.g., persons per square mile, BTUs per cubic foot).
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1. I can describe a typographical grid system.
2. I can 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).
3. I can create a visual representation of a design problem
4. I can focus on situations well modeled by trigonometric ratios for acute angles.
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I can use points, lines and planes to define other geometric terms (such as angles, line segments, perpendicular lines, etc) and use "if then" and "If and only if" statements to describe the terms.
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I can explain and justify the steps of a construction.
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Unit 1: Transformations, Similarity, & Congruence
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I can identify translations, reflections, rotations, and compositions
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I can perform transformations in the coordinate plane with and without technology
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I can use (x,y) rules to perform transformations
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I can develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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I can draw the preimage and image of a rotation, reflection, or translation with and without technology.
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I can specify a sequence of transformations that will carry a given figure onto another.
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I can identify rotational and reflection symmetries of polygons
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I can define image, pre-image, scale factor, center, and similar figures as they relate to transformations.
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I can identify a dilation stating its scale factor and center
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I can perform a dilation
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I can explain that the scale factor represents how many times longer or shorter a dilated line segment is than its pre-image.
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I can verify experimentally that a dilation takes a line not passing through the center of the dilation to a parallel line by showing the lines are parallel.
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I can verify experimentally that dilation leaves a line passing through the center of the dilation unchanged by showing that it is the same line
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I can verify that a dilated image is similar to its pre-image by showing congruent angles and proportional sides
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I can determine when transformations are isometries
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i can use similarity transformations to explain that two triangles are similar iff all pairs of corresponding angles are congruent and corresponding pairs of sides are proportional
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i can determine if two figures are similar, and explain why
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I can construct congruent angles using appropriate geometric construction tools
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I can construct angle bisectors using appropriate geometric construction tools.
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I can construct congruent segments using appropriate geometric construction tools.
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I can prove that opposite angles in a parallelogram are congruent.
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I can prove that opposite sides of a parallelogram are congruent.
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I can prove the diagonals of a parallelogram bisect each other.
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I can prove rectangles are parallelograms with congruent diagonals.
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I can use coordinates to prove simple geometric theorems algebraically....given 4 points prove what shape it is using distance formula
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I can apply the properties of slope to solve geometric problems involving parallel and perpendicular lines....prove sides of quadrilateral are parallel or perpendicular
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I can compute perimeters and areas of polygons.
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I can construct parallel lines using appropriate geometric construction tools.
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I can construct perpendicular lines using appropriate geometric construction tools.
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I can construct congruent segments using appropriate geometric construction tools.
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Unit 2: Triangles, Proof, & Similarity
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I can determine if two figures (triangles) are congruent based on the definition of congruence in terms of rigid motions (distance and angle measure preserved).
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I can explain how the criteria for triangle congruence (ASA, SAS, SSS) follows from the definition of congruence in terms of rigid motions (i.e. if two angles and the included side of one triangle are transformed by the same rigid motion(s) then the triangle image will be congruent to the original triangle).
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I can use dynamic geometry software or straightedge and compass to verify criteria for triangle congruence (ASA, SAS, SSS)
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I can use sufficient conditions to prove triangles are congruent
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I can prove that vertical angles are congruent.
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I can prove that special angle pairs are congruent when given two parallel lines cut by a transversal.
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I can prove that the points on a perpendicular bisector are equidistant from a segment's endpoints
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I can prove that the sum of the interior angles of a triangle is 180 degrees
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I can prove that the base angles of an isosceles triangle are congruent.
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I can the prove that the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length
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I can the prove that the medians of a triangle meet at a common point.
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I can establish the AA criterion for similarity of triangles by extending the properties of similarity transformations to the general case of any two similar triangles.
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I can prove a line parallel to one side of a triangle divides the other two sides proportionally.
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I can prove the Pythagorean Theorem proved using triangle similarity.
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I can use congruency and similarity for triangles to prove relationships in geometric figures and solve problems
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I can construct congruent angles using appropriate geometric construction tools.
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I can construct congruent segments using appropriate geometric construction tools.
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I can construct parallel lines using appropriate geometric construction tools.
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I can construct perpendicular lines using appropriate geometric construction tools.
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I can construct a segment bisector using appropriate geometric construction tools.
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I can construct angle bisectors using appropriate geometric construction tools.
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I can use common ratios of sides for similar right triangles and develop a relationship between the ratio and the acute angle leading to the trigonometry ratios of sin, cos & tan.
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I can explain how the sine and cosine of complementary angles are related to each other.
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I can solve for an unknown angle or side of a right triangle using sine, cosine, and tangent and their inverses.
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I can apply right triangle trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
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I can calculate a point on a line segment provided a given ratio.
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I can derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
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1. I can use the Laws of Sines and Cosines to find missing angles or side length measurements.
2. I can prove the Law of Sines
3. I can prove the Law of Cosines
4. I can recognize when the Law of Sines or Law of Cosines can be applied to a problem and solve problems in context using them.
5. I can, with respect to the general case of Laws of Sines and Cosines, extended the definition of sine and cosine to obtuse angles.
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1. I can determine from given measurements in right and non-right triangles whether it is appropriate to use the Law of Sines or Cosines.
2. I can apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
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Unit 3: Circles, Proofs and Constructions
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I can write the equation of a circle of a given center and radius using the Pythagorean Theorem.
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I can identify the center and radius of a circle given its equation
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I can prove that all circles are similar using dilation.
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I can use coordinates to prove simple geometric theorems algebraically...prove a point lies on a circle
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I can identify and describe relationships among central angles, inscribed angles, arcs, radii, and chords
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I can identify, describe and solve for variables involving radii, secants, tangents, arcs, chords, and inscribed angles.
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I can construct an equilateral triangle inscribed in a circle.
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I can construct a square inscribed in a circle.
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I can construct a hexagon inscribed in a circle.
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I can construct the inscribed and circumscribed circles of a triangle.
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I can prove properties of angles for a quadrilateral inscribed in a circle.
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I can show the proportionality of the length of the arc and the radius as the radian measure of the angle.
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I can calculate the length of an arc
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I can derive the formula for the area of a sector and apply it
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I can use dissection arguments on regular polygon and its area (A=1/2 * apothem * perimeter) to describe circumference and areas of circles (a circle is ~infinite-gon)
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I can construct a tangent line from a point outside a given circle to the circle.
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I can write the equation of a parabola given appropriate info
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I can write the equation of an ellipse or hyperboal given appropriate info
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Unit 4: Extending to Three Dimensions
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I can use Cavalieri's principle and dissection arguments to informally describe volumes of cylinders, prisms, pyramids, cones.
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I can calculate the surface area and volume of cylinders, prisms, pyramids, cones and spheres.
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I can describe the cross-sections of three dimensional figures.
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I can use Cavalieri's principle to describe the formula for volume of a sphere
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