### GEO-G: Geometry

#### GEO-G.CO: Congruence

1.1.1: Experiment with transformations in the plane.

GEO-G.CO.1: Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.

GEO-G.CO.2: Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.

GEO-G.CO.3: Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.

GEO-G.CO.4: Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.

GEO-G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.

1.1.2: Understand congruence in terms of rigid motions.

GEO-G.CO.6: 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.

GEO-G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.

1.1.3: Prove geometric theorems

GEO-G.CO.9: Prove and apply theorems about lines and angles.

GEO-G.CO.10: Prove and apply theorems about triangles.

GEO-G.CO.11: Prove and apply theorems about parallelograms.

1.1.4: Make geometric constructions.

GEO-G.CO.12: Make, justify, and apply formal geometric constructions.

GEO-G.CO.13: Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.

#### GEO-G.SRT: Similarity, Right Triangles, and Trigonometry

1.2.1: Understand similarity in terms of similarity transformations.

GEO-G.SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor.

GEO-G.SRT.1.a: Verify experimentally that dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

GEO-G.SRT.1.b: Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

GEO-G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

GEO-G.SRT.3: Use the properties of similarity transformations to establish the AA~, SSS~, and SAS~ criterion for two triangles to be similar.

1.2.2: Prove theorems involving similarity.

GEO-G.SRT.4: Prove and apply similarity theorems about triangles.

GEO-G.SRT.5: Use congruence and similarity criteria for triangles to:

GEO-G.SRT.5.a: Solve problems algebraically and geometrically.

GEO-G.SRT.5.b: Prove relationships in geometric figures.

1.2.3: Define trigonometric ratios and solve problems involving right triangles.

GEO-G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent ratios for acute angles.

GEO-G.SRT.8: Use sine, cosine, tangent, the Pythagorean Theorem and properties of special right triangles to solve right triangles in applied problems.

#### GEO-G.C: Circles

1.3.1: Understand and apply theorems about circles.

GEO-G.C.2a: Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.

GEO-G.C.2b: Identify, describe and apply relationships among radii, chords, tangents, and secants of a circle.

1.3.2: Find arc lengths and area of sectors of circles.

GEO-G.C.5: Using proportionality, find one of the following given two others: the central angle, arc length, radius or area of sector.

#### GEO-G.GPE: Expressing Geometric Properties with Equations

1.4.1: Translate between the geometric description and the equation of a conic section.

GEO-G.GPE.1a: Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Find the center and radius of a circle, given the equation of the circle.

GEO-G.GPE.1b: Graph circles given their equations.

1.4.2: Use coordinates to prove simple geometric theorems algebraically.

GEO-G.GPE.5: On the coordinate plane:

GEO-G.GPE.5.b: Determine if lines are parallel, perpendicular, or neither, based on their slopes; and

GEO-G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

#### GEO-G.GMD: Geometric Measurement and Dimension

1.5.1: Explain volume formulas and use them to solve problems.

GEO-G.GMD.1: Provide informal arguments for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

GEO-G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Correlation last revised: 9/15/2020

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