# Geometry

### Parents, please note that these standards are listed in the order, and for the amount of time, that most Beyond Textbooks schools follow. These are guidelines, and your child's school may vary.

#### Benchmark 1:

1. Geo.M.G.CO.A.01: I will be able to define an angle, circle, perpendicular lines, parallel lines, and line segments using the definition of a point, and the distance along a line and a curve, and identify real world examples. - 5 Days
2. Geo.M.G.CO.D.12: I can construct various geometric objects using a variety of tools and methods. - 5 Days
3. Geo.M.G.GPE.B.05: Using slope, I will be able to algebraically determine if lines are parallel or perpendicular to help me solve geometric problems. - 5 Days
4. Geo.M.G.CO.C.09: Given parallel lines and a transversal, I will be able to prove theorems such as: alternate interior angles are congruent; vertical angles are congruent; consecutive interior angles are supplementary. I will be able to apply theorems in real world context. - 5 Days
5. Geo.M.G.CO.A.04: I will develop definitions of transformations using how they relate to angles, circles, perpendicular and parallel lines and line segments, and use transformation properties to identify and justify the transformation that maps an image to a pre-image. - 5 Days
6. Geo.M.G.CO.A.05: I will be able to do 2 or more transformations on a figure and identify the single or series of transformations, in order, that map a pre-image to an image. - 5 Days
7. Geo.M.G.GPE.B.07: I can use coordinates to find the perimeter and area of a polygon. - 5 Days

#### Benchmark 2:

1. Geo.M.G.CO.B.08: I can explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions, and explain why SSA and AAA are not enough evidence for triangle congruence. - 5 Days
2. Geo.M.G.CO.C.10: I can prove theorems about triangles, and apply them in a real world context. - 5 Days
3. Geo.M.G.SRT.A.01: I can prove the properties of dilations. - 5 Days
4. Geo.M.G.SRT.A.02: Given two figures, I can use the definition of similarity to decide if the two figures are similar; I can explain the proportionality of corresponding sides and the equality of corresponding angles of similar figures by using similarity transformations. - 5 Days
5. Geo.M.G.SRT.B.04: I can prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. - 10 Days
6. Geo.M.G.SRT.B.05: I can use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures. - 10 Days
7. Geo.M.G.SRT.C.06: I can solve problems using sine, cosine, and tangent ratios of the acute angles of a right triangle. * These ratios are the same for the acute angles of similar right triangles. I will also know the reciprocal ratios for sine, cosine, and tangent. - 5 Days

#### Benchmark 3:

1. Geo.M.G.SRT.C.08: I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. - 5 Days
2. Geo.M.G.CO.C.11: I will prove the validity of parallelogram theorems. - 5 Days
3. Geo.M.G.GPE.B.04: I can use the coordinate geometry, such as the slope and distance formulas, to prove simple geometric theorems. - 5 Days
4. Geo.M.G.C.A.02: I can identify and describe relationships among inscribed angles, radii, and chords. I can solve for arc and chord length and angles. - 5 Days
5. Geo.M.G.C.B.05: I can derive and use the formula to find the length of a given arc and the area of a given sector. - 5 Days
6. Geo.M.G.GPE.A.01: I can write the equation of a circle in center radius form, given the standard form equation of a circle, I can use the equation of a circle to find the radius and center point of a circle. - 5 Days
7. Geo.M.G.GMD.A.03:  I can use volume formulas for cylinders, pyramids, cones and spheres to solve problems. - 10 Days

#### Benchmark 4:

1. Geo.M.G.MG.A.01: I can model objects using geometric shapes. - 5 Days
2. Geo.M.G.MG.A.02: I can apply concepts of density based on area and volume to model real world and mathematical problems. - 5 Days
3. Geo.M.G.MG.A.03: I can apply geometric methods to solve design problems in real world problems. - 5 Days
4. Geo.M.G.SRT.D.11: I can apply the law of cosines and sines to find the missing sides and angles of triangles. - 5 Days

1. Geo.M.G.CO.A.02: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations 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 (e.g., translation versus horizontal stretch). (Month 2)
2. Geo.M.G.CO.A.03: Given a rectangle, parallelogram, trapezoid, or regular polygons, describe the rotations and reflections that carry it onto itself. (Month 2)
3. Geo.M.G.CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. (Month 2)
4. Geo.M.G.GPE.B.06: Find the point on a directed line segment between two given points that partitions the segment into a given ratio. (Month 3 & 4)
5. Geo.M.G.CO.B.06: 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. (Month 4)
6. Geo.M.G.CO.B.07: 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. (Month 4)
7. Geo.M.G.SRT.A.03: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (Month 5)
8. Geo.M.G.SRT.C.07: Explain and use the relationship between the sine and cosine of complementary angles. (Month 5)
9. Geo.M.G.C.A.01: Prove that all circles are similar. (Month 7 & 8)
10. Geo.M.G.C.A.03: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. (Month 7 & 8)
11. Geo.M.G.C.A.04: Construct a tangent line from a point outside a given circle to the circle. (Month 7 & 8)
12. Geo.M.G.GMD.A.01: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. (Month 8 & 9)
13. Geo.M.G.GMD.A.02: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. (Month 10)
14. Geo.M.G.GMD.B.04: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. (Month 10)
15. Geo.M.G.SRT.D.09: 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. (Month 10)
16. Geo.M.G.SRT.D.10: Prove the Laws of Sines and Cosines and use them to solve problems. (Month 10)

#### Yearly Standards:

• None
08:31, 2 Dec 2016

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