**CCGPS Analytic Geometry Unit 3: Modeling Geometry**

Unit Plan:

__Pre-requisite Knowledge Required:__

*·Students understand the definition of functions and mapping them in the Cartesian plane (MCC9-12.A.REI.10)*

·Students understand how to perform transformation of objects and functions in the Cartesian plane (MCC9-12.F.BF.3, MCC9-12.G.CO.2, MCC9-12.G.CO.3, MCC9-12.G.SRT.1)

· Knowledge of the shape of a cone. (MCC9-12.G.GMD.3)

·Understand linear equations and quadratic equations from an algebraic and geometric perspective (MCC9-12.A.SSE.1, MCC9-12.A.SSE.2, MCC9-12.A.CED.1, MCC9-12.F.IF.2)

·Understand and interpret key features such as roots or zeros in context of a function (MCC9-12.F.IF.4, MCC9-12.A.CED.1, MCC9-12.A.CED.2)

·Interpret linear and quadratic equations in context (MCC9-12.A.SSE.1, MCC9-12.A.CED.1, MCC9-12.A.CED.2)

·Understand solving a system containing two linear equations or solving a linear equation (MCC9-12.A.REI.1, MCC9-12.A.REI.3, MCC9-12.A.REI.5, MCC9-12.A.REI.6, MCC9-12.A.REI.11)

·Understand how to graph a linear and quadratic function (MCC9-12.F.IF.7, MCC9-12.F.IF.9, MCC9-12.F.BF)

·Understand how to find the zeros of a parabola using the Zero Product Property and various methods such as factoring, completing the square, or using the quadratic formula. (MCC9-12.N.CN.7, MCC9-12.A.SSE.3)

·Knowledge of the Pythagorean theorem (MCC9-12.G.SRT.8)

·Knowledge of vertex, factored, and standard forms of parabolic equations and how to convert between each (MCC9-12.A.SSE.3, MCC9-12.A.CED.4)

· Knowledge of calculating the slope of a line and distance formula. Compute perimeters and areas of polygons (triangles and rectangles) using the distance formula. (MCC9-12.F.IF.6, MCC9-12.G.GPE.7)

· Know definitions of angle, circle, perpendicular/parallel line, and line segment and develop definitions of rotations, reflections, and translations in terms of these objects. Using these transformation definitions, depict a transformed geometric figure using technology. (MCC9-12.G.CO.1, MCC9-12.G.CO.4, MCC9-12.G.CO.5)

·Understand the slope criteria definition for parallel and perpendicular lines. (MCC9-12.G.GPE.5)

·Find the point on a directed line segment between two given points that partitions the segment in a given ratio. (MCC9-12.G.GPE.6)

·Understand exponent property rules (MCC9-12.N.RN.2, MCC9-12.A.APR.1)

·Understand rational, irrational, and complex numbers in terms of zeros of a quadratic equation. (MCC9-12.N.RN.1, MCC9-12.N.RN.2, MCC9-12.N.RN.3, MCC9-12.N.CN.1, MCC9-12.N.CN.2, MCC9-12.N.CN.7)

·Understand the concept of similarity between two figures and explain using transformations. Use these properties to prove two triangles are similar (MCC9-12.G.SRT.2, MCC9-12.G.SRT.3)

·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 (MCC9-12.G.SRT.4)

· Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and predict the effect. Understand and use ASA, SAS, and SSS. (MCC9-12.G.SRT.5, MCC9-12.G.CO.6, MCC9-12.G.CO.7, MCC9-12.G.CO.8)

·Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. (MCC9-12.G.CO.9)

·Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point (MCC9-12.G.CO.10)

·Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Make geometric constructions (MCC9-12.G.CO.11)

·Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. (MCC9-12.G.CO.13)

·Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. (MCC9-12.G.SRT.6)

·Explain and use the relationship between the sine and cosine of complementary angles (MCC9-12.G.SRT.7)

·Prove that all circles are similar. (MCC9-12.G.C.1)

·Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. (MCC9-12.G.C.2)

·Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. (MCC9-12.G.C.3)

·Construct a tangent line from a point outside a given circle to the circle. Find arc lengths and areas of sectors of circles (MCC9-12.G.C.4)