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Geometry Proficiencies 1. Apply the midpoint formula to solve problems in a coordinate plane. I can… Where can I find help? I can find the midpoint of two points on a number line (1-D). http://www.khanacademy.org/math/algebra/linear-equationsand-inequalitie/v/midpoint-formula I can find the midpoint to two points on a coordinate plane (2-D). 2. Identify, apply, and analyze angle relationships among two or more lines and a transversal to determine if lines are parallel, perpendicular, or neither. I can identify when angles have the following relations: vertical angles, linear pair, alternate interior angles, alternate exterior angles, corresponding angles, consecutive interior angles. I can determine the measure of all eight angles formed when given parallel lines cut by a transversal. http://www.khanacademy.org/math/geometry/angles/v/anglesat-the-intersection-of-two-lines http://www.khanacademy.org/math/geometry/angles/v/anglesformed-between-transversals-and-parallel-lines http://www.khanacademy.org/math/geometry/angles/v/anglesof-parallel-lines-2 http://www.khanacademy.org/math/geometry/angles/v/angles-part-3 http://www.khanacademy.org/math/geometry/angles/v/theangle-game 3. Apply theorems, properties, and definitions to determine, identify, and justify congruency or similarity of triangles and classify quadrilaterals. I can justify congruence of triangles using SSS, SAS, ASA and AAS. I can write congruence statements of two congruent shapes. http://www.khanacademy.org/math/geometry/triangles/v/congr uent-and-similar-triangles http://www.khanacademy.org/math/geometry/triangles/v/congr uent-triangles-and-sss http://www.khanacademy.org/math/geometry/triangles/v/other -triangle-congruence-postulates http://www.khanacademy.org/math/geometry/angles/v/moreon-why-ssa-is-not-a-postulate http://www.khanacademy.org/math/geometry/triangles/v/findin g-congruent-triangles http://www.khanacademy.org/math/geometry/triangles/v/congr uent-triangle-proof-example www.khanacademy.org/math/geometry/triangles/v/congruenttriangle-example-2 4. Apply theorems of corresponding parts of congruent and similar figures to determine missing sides and angles of polygons. I can determine side lengths and angles measures based on triangles being similar. I can determine missing side lengths and angle measures based on triangles being congruent. http://www.khanacademy.org/math/geometry/triangles/v/simila r-triangle-basics http://www.khanacademy.org/math/geometry/triangles/v/simila rity-postulates http://www.khanacademy.org/math/geometry/triangles/v/simila r-triangles http://www.khanacademy.org/math/geometry/triangles/v/simila r-triangles--part-2 http://www.khanacademy.org/math/geometry/triangles/v/simila r-triangle-example-problems http://www.khanacademy.org/math/geometry/triangles/v/simila rity-example-problems http://www.khanacademy.org/math/geometry/triangles/v/appli cation-of-similar-triangles 5. Recognize and identify line and rotational symmetry of two dimensional figures. (To exceed classify freeze groups) I can identify lines of reflection http://www.mathsisfun.com/geometry/symmetry-reflection.html of two dimensional shapes. http://en.wikipedia.org/wiki/Rotational_symmetry I can identify the angle of rotational symmetry of two http://www.mathsisfun.com/geometry/symmetrydimensional shapes. rotational.html (to exceed) I can classify horizontal repeating patterns as one of the 7 frieze groups. http://mathdl.maa.org/images/upload_library/4/vol1/architectur e/Math/seven.html http://euler.slu.edu/escher/index.php/Frieze_Patterns#The_Se ven_Frieze_Groups 6. Identify and perform single and multiple transformations of geometric figures in a plane, including translations, origincentered dilations, reflections across either axis or y = + - x, and rotations about the origin in multiples of 90 degrees. I can perform single transformations on shapes composed of ordered pairs. http://www.mathsisfun.com/geometry/transformations.html I can perform multiple transformations on shapes composed of ordered pairs. http://www.mathsisfun.com/geometry/reflection.html http://www.mathsisfun.com/geometry/rotation.html http://www.mathsisfun.com/geometry/translation.html I can identify the type of http://www.mathsisfun.com/activity/shapes-symmetry.html transformation performed on a shape. (reflection, rotation, translation/slide, and glide see handouts reflection) 7. Express square roots in equivalent radical form and their decimal approximations when appropriate. Also explore higher order roots. I can simplify square roots (camp gitagoomee). http://www.khanacademy.org/math/algebra/exponentsradicals/v/understanding-square-roots I can use a calculator to get a decimal approximation of a square root. http://www.khanacademy.org/math/algebra/exponentsradicals/v/approximating-square-roots I can simplify higher order roots like cube roots. I can rationalize the denominator. (I can get the radical out of the denominator.) http://www.khanacademy.org/math/algebra/exponentsradicals/v/square-roots-and-real-numbers http://www.khanacademy.org/math/algebra/exponentsradicals/v/simplifying-square-roots http://www.khanacademy.org/math/algebra/polynomials/v/r ationalizing-denominators-of-expressions 8. Use the Pythagorean Theorem to solve for unknown lengths in right triangles and the distance formula. (Determine the missing dimensions of Special Right Triangles) I can find the length of a side (leg) of a right triangle when given another side (leg) and the hypotenuse. I can find the length of the hypotenuse of a right triangle when given the two other sides (legs). I can use the distance formula to find the distance between two sets of ordered pairs. I can use the 45-45-90 and 30-60-90 special right triangles to find the lengths of unknown sides of similar triangles. http://www.khanacademy.org/math/geometry/triangles/v/introd uction-to-the-pythagorean-theorem http://www.khanacademy.org/math/geometry/triangles/v/thepythagorean-theorem http://www.khanacademy.org/math/geometry/triangles/v/pytha gorean-theorem-ii http://www.khanacademy.org/math/algebra/linear-equationsand-inequalitie/v/distance-formula http://www.khanacademy.org/math/geometry/triangles/v/4545-90-triangles http://www.khanacademy.org/math/geometry/triangles/v/4545-90-triangle-side-ratios http://www.khanacademy.org/math/geometry/triangles/v/introto-30-60-90-triangles http://www.khanacademy.org/math/geometry/triangles/v/3060-90-triangles-ii http://www.khanacademy.org/math/geometry/triangles/v/3060-90-triangle-side-ratios-proof http://www.khanacademy.org/math/geometry/triangles/v/3060-90-triangle-example-problem 9. Use Trig ratios to solve for unknown lengths in right triangles. I can use trigonometric ratios to determine unknown lengths of the sides of right triangles. (when given one angle and one side) http://www.khanacademy.org/math/trigonometry/v/basictrigonometry I can use trigonometric ratios to determine unknown angles of a right triangle. (when given two sides) http://www.khanacademy.org/math/trigonometry/v/using-trigfunctions http://www.khanacademy.org/math/trigonometry/v/basictrigonometry-ii http://www.khanacademy.org/math/trigonometry/v/using-trigfunctions-part-ii http://www.khanacademy.org/math/trigonometry/v/trigonometr y-word-problems--part-1 http://www.khanacademy.org/math/trigonometry/v/trigonometr y-word-problems--part-2 http://www.khanacademy.org/math/trigonometry/e/law_of_cos ines http://www.khanacademy.org/math/trigonometry/v/law-ofcosines 10. Determine if three given lengths form a triangle. If the given lengths form a triangle, classify it as acute, right, or obtuse. I can determine if three given lengths can make a triangle. http://www.geom.uiuc.edu/~wanous/definitionofatriangle.html http://www.apluspublishing.com/aplus4.html I can determine if a triangle is a right, obtuse or acute triangle. I can determine if a right triangle is a special right triangle. http://www.wikihow.com/Determine-if-Three-Side-LengthsAre-a-Triangle http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri30. htm http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri45. htm 11. Determine the missing dimensions, angles, or area of quadrilaterals, triangles, circles, composite shapes, and shaded regions. I can determine the area of quadrilaterals, triangles, circles, composite shapes and shaded regions. http://www.khanacademy.org/math/geometry/basic-geometry/v/perimeterand-area-basics I can determine missing dimensions of the above shapes when given the area and some of the dimensions. http://www.khanacademy.org/math/geometry/basic-geometry/v/perimeterand-area-of-a-non-standard-polygon http://www.khanacademy.org/math/geometry/basic-geometry/v/area-andperimeter http://www.khanacademy.org/math/geometry/polygons-quadsparallelograms/v/quadrilateral-overview http://www.khanacademy.org/math/geometry/circles-topic/v/circles--radius-diameter-and-circumference http://www.khanacademy.org/math/geometry/circles-topic/v/area-of-acircle http://www.khanacademy.org/math/geometry/triangles/v/triang le-area-proofs 12. Identify, classify, model, sketch, and label representations of three-dimensional objects from nets and from different perspectives. I can identify and classify three dimensional shapes from nets. http://www.primaryresources.co.uk/maths/mathsE3.htm#3 http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/ 3d/index.htm I can sketch a net of any three dimensional shape. http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=we b&cd=4&ved=0CDMQFjAD&url=http%3A%2F%2Fcollege.cen gage.com%2Fmathematics%2Fbassarear%2Felementary_sc hool%2F3e%2Fstudents%2Fsample%2Fch08_03.pdf&ei=jKIUP3aAo6UjAKX4YCgAg&usg=AFQjCNHOS0XO4MCgzWMh knlXMTILgz0_Wg 13. Identify and apply formulas for surface area and volume of spheres, right solids, including rectangular prisms and pyramids; cones; and cylinders; and compositions thereof. Solve related context-based problems. I can determine the surface area of rectangular prisms and pyramids; cones; and cylinders and compositions thereof. I can determine the volume of rectangular prisms and pyramids; cones; and cylinders and compositions thereof. http://www.khanacademy.org/math/geometry/basic-geometry/v/solidgeometry-volume http://www.khanacademy.org/math/geometry/basic-geometry/v/cylindervolume-and-surface-area http://www.khanacademy.org/math/geometry/basic-geometry/v/volume-ofa-sphere 14. Identify and apply formulas to solve for the missing dimensions of spheres and right solids, including rectangular prisms and pyramids, cones, and cylinders, both numerically and symbolically. I can determine unknown dimensions of rectangular prisms and pyramids; cones; and cylinders and compositions thereof when given the surface area or volume. http://www.khanacademy.org/math/geometry/basic-geometry/v/solidgeometry-volume http://www.khanacademy.org/math/geometry/basic-geometry/v/cylindervolume-and-surface-area http://www.khanacademy.org/math/geometry/basic-geometry/v/volume-ofa-sphere 15. Apply a scale factor to determine similar two- and threedimensional figures, are similar. Compare and compute their respective areas and volume of similar figures. I can determine the scale factor, ratio of areas and ratio of volumes when given one of the fore mentioned. I can use the scale factor to an unknown dimension of two similar objects. I can use the ratio of areas to find the unknown area of one of two similar objects. I can use the ratio of volumes to find the unknown volume of one of two similar objects. http://www.khanacademy.org/math/algebra/ck12-algebra1/v/scale-and-indirect-measurement Bonus #1. In problems involving circles, apply theorems and properties of chords, tangents, and angles; and theorems and formulas of arcs and sectors. I can find lengths of chords, arcs and tangent lines when given enough information. (enough being all but one part of theorems of circles). I can find angles formed by chords, arcs and tangent lines when given enough information. http://www.khanacademy.org/test-prep/california-standardstest/geometry-2/v/ca-geometry--circle-area-chords-tangent