# Geometry

## Geometry Standards

##### Quarter 1 Standards:
1. Geo.M.G.CO.A.01: The Highly Proficient student can explain the definition of an angle, circle, perpendicular lines, parallel lines and identify real-world examples of each figure.

2. Geo.M.G.CO.A.02: The Highly Proficient student can represent and describe transformations in the plane as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not.

3. Geo.M.G.CO.A.03: Given a rectangle, parallelogram, trapezoid, or regular polygons, the Highly Proficient student can describe the rotations and reflections that carry it onto itself.

4. Geo.M.G.CO.A.04: The Highly Proficient student can represent functions to describe transformations using a variety of media and justify statements about rotations, reflections, and translations on the coordinate plane.

5. Geo.M.G.CO.A.05: The Highly Proficient student can perform 2 or more transformations on a figure, identify the single or series of transformations that map a pre-image to an image, and explain how the order of a sequence of transformations being performed may result in different outcomes.

6. Geo.M.G.CO.C.09: The Highly Proficient student can prove theorems such as: alternate interior angles are congruent; vertical angles are congruent; consecutive interior angles are supplementary and apply theorems in real-world context.

7. Geo.M.G.CO.D.12: The Highly Proficient student can construct various geometric objects using a variety of tools and methods.

8. Geo.M.G.CO.D.13: The Highly Proficient student can construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle; with a variety of tools and methods.

9. Geo.M.G.GPE.B.05: The Highly Proficient student can create the equation of a line parallel or perpendicular to a given line that passes through a given point in a context.

10. Geo.M.G.GPE.B.07: The Highly Proficient student can use coordinates to find the perimeter of polygons and area of triangles and rectangles, and apply them to real-world problems.

##### Quarter 2 Standards:
1. Geo.M.G.CO.B.06: The Highly Proficient student can use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

2. Geo.M.G.CO.B.07: The Highly Proficient student can 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.

3. Geo.M.G.CO.B.08: The Highly Proficient student can demonstrate how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions; understands and explains why SSA and AAA are not enough evidence for triangle congruence.

4. Geo.M.G.CO.C.10: The Highly Proficient student can prove theorems about triangles, and apply them in a real-world context. Theorems include: triangle sum theorem, base angles theorem, midsegment theorem, and the medians of a triangle meet at a point.

5. Geo.M.G.GPE.B.06: The Highly Proficient student can find the point on a directed line segment between two given points that partitions the segment into a given ratio.

6. Geo.M.G.SRT.A.01: The Highly Proficient student can verify the properties of dilations and locate the center of dilation and find the scale factor given a pair of similar figures on a coordinate plane.

7. Geo.M.G.SRT.A.02: The Highly Proficient student can prove or disprove that two given figures are similar, using transformations and the definitions of similarity.

8. Geo.M.G.SRT.B.04: The Highly Proficient student can prove theorems about triangles, and apply them in a real-world context. Theorems include: triangle proportionality theorem and converse and the Pythagorean Theorem proved using triangle similarity.

9. Geo.M.G.SRT.B.05: The Highly Proficient student can solve problems and prove conjectures about congruence or similarity in geometric figures, in a real-world context using congruence and similarity criteria for triangles.

10. Geo.M.G.SRT.C.06: The Highly Proficient student can determine the similarity of right triangles by comparing the trigonometric ratios of the corresponding sides and solve for missing angles of right triangles using sine and cosine.

##### Quarter 3 Standards:
1. Geo.M.G.C.A.01: The Highly Proficient student can prove that all circles are similar.

2. Geo.M.G.C.A.02: The Highly Proficient student can solve problems using relationships among inscribed angles, radii, and chords in circles.

3. Geo.M.G.C.A.03: The Highly Proficient student can construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

4. Geo.M.G.C.A.04: The Highly Proficient student can construct a tangent line from a point outside a given circle to the circle.

5. Geo.M.G.C.B.05: The Highly Proficient student can prove that the length of the arc intercepted by an angle is proportional to the radius, with the radian measure of the angle being the constant of proportionality. The Highly Proficient student can convert between degrees to radians.

6. Geo.M.G.CO.C.11: The Highly Proficient student can prove theorems about parallelograms and apply them in a real-world context.

7. Geo.M.G.GMD.A.03:  The Highly Proficient student can find the volume of cylinders, pyramids, cones, and spheres in real-life context.

8. Geo.M.G.GPE.A.01: The Highly Proficient student can write the equation of a circle in center-radius form, given center and radius, given points of tangency, and by completing the square.

9. Geo.M.G.GPE.B.04: The Highly Proficient student can use coordinates to prove or disprove simple geometric relationships and theorems algebraically and construct visual representations on the coordinate plane that meet given conditions.

10. Geo.M.G.SRT.A.03: The Highly Proficient student can use the properties of similarity transformations to establish the AA, SAS, and SSS criterion for two triangles to be similar.

11. Geo.M.G.SRT.C.07: The Highly Proficient student can explain and use the relationship between the sine and cosine of complementary angles.

12. Geo.M.G.SRT.C.08: The Highly Proficient student can model solutions to situations, using trigonometric ratios and the Pythagorean Theorem, by constructing equations that can be used to solve the problem.

##### Quarter 4 Standards:
1. Geo.M.G.GMD.A.01: The Highly Proficient student can analyze and verify the formulas for the volume of a cylinder, pyramid, and cone.

2. Geo.M.G.GMD.A.02: The Highly Proficient student can give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

3. Geo.M.G.GMD.B.04: The Highly Proficient student can identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

4. Geo.M.G.MG.A.01: The Highly Proficient student can use composite geometric shapes, measures, and properties to model and describe objects.

5. Geo.M.G.MG.A.02: The Highly Proficient student can apply concepts of density based on area and volume to model real-world and mathematical problems.

6. Geo.M.G.MG.A.03: The Highly Proficient student can design a composite structure to meet constraints and optimization requirements.

7. Geo.M.G.SRT.D.09: The Highly Proficient student can derive the formula A  = ó ab  sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

8. Geo.M.G.SRT.D.10: The Highly Proficient student can prove the Laws of Sines and Cosines and use them to solve problems.

9. Geo.M.G.SRT.D.11: The Highly Proficient student can apply the law of cosines and sines to find the missing sides and angles of triangles.

##### Quarter 4 Standards (taught throughout the year):
1. Geo.M.G.N.Q.A.01: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data display, include utilizing real-real-world context.

2. Geo.M.G.N.Q.A.02: Define appropriate quantities for the purpose of descriptive modeling. Include problem-solving opportunities utilizing real-real-world context.

3. Geo.M.G.N.Q.A.03: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities utilizing real-real-world context.

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