CA High School Geometry Curriculum

CA High School Geometry Curriculum

• CA.G.G.CO.1Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
  • Parallel and perpendicular line segments
  • Central and inscribed angles in circles
• CA.G.G.CO.2Represent 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.
  • Introduction to transformations
  • Rotational symmetry and transformations
  • Scale diagrams
  • Similar polygons
• CA.G.G.CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • Trapezoids, rhombi, and kites
  • Polygons
  • Complex polygons
• CA.G.G.CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • Line symmetry
  • Perpendicular line proofs
• CA.G.G.CO.6Use 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.
  • Congruence and congruent triangles
  • Classifying triangles
• CA.G.G.CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
  • Triangles congruent by SSS proofs
  • Triangles congruent by SAS and HL proofs
  • Triangles congruent by ASA and AAS proofs
• CA.G.G.CO.9Prove theorems about lines and angles.
  • Parallel lines and transversals
  • Parallel line proofs
  • Pairs of lines and angles
• CA.G.G.CO.10Prove theorems about triangles.
  • Isosceles and equilateral triangles
• CA.G.G.CO.11Prove theorems about parallelograms.
  • Parallelograms
• CA.G.G.SRT.1Verify experimentally the properties of dilations given by a center and a scale factor.
  • Enlargements and reductions with scale factors
• CA.G.G.SRT.2Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • Similar triangles
• CA.G.G.SRT.4Prove theorems about triangles.
  • Pythagorean theorem
  • Estimating square roots
  • Using the pythagorean relationship
  • Applications of pythagorean theorem
• CA.G.G.SRT.6Understand 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.
  • Use sine ratio to calculate angles and sides (Sin = o / h)
  • Use tangent ratio to calculate angles and sides (Tan = o / a)
• CA.G.G.SRT.7Explain and use the relationship between the sine and cosine of complementary angles.
  • Use cosine ratio to calculate angles and sides (Cos = a / h)
  • Quotient identities and reciprocal identities
  • Pythagorean identities
  • Sum and difference identities
  • Double-angle identities
  • Cofunction identities
• CA.G.G.SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
  • Combination of SohCahToa questions
  • Word problems relating ladder in trigonometry
  • Word problems relating guy wire in trigonometry
  • Other word problems relating angles in trigonometry
• CA.G.G.SRT.8.1Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90° and 45°, 45°, 90°).
  • Solving expressions using 45-45-90 special right triangles
  • Solving expressions using 30-60-90 special right triangles
• CA.G.G.SRT.9(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • Area of triangles: 1/2 a*b sin(C)
• CA.G.G.SRT.10(+) Prove the Laws of Sines and Cosines and use them to solve problems.
  • Law of sines
  • Law of cosines
• CA.G.G.SRT.11(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
  • Applications of the sine law and cosine law
• CA.G.G.C.1Prove that all circles are similar.
  • Central angles and proofs
• CA.G.G.C.2Identify and describe relationships among inscribed angles, radii, and chords.
  • Inscribed angles and proofs
• CA.G.G.C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
  • Circle chord, tangent, and inscribed angles proofs
• CA.G.G.C.5Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians.
  • Arcs of a circle
  • Areas and sectors of circles
  • Converting between degrees and radians
  • Trigonometric ratios of angles in radians
  • Radian measure and arc length
• CA.G.G.GPE.1Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  • Conics - Circle
• CA.G.G.GPE.2Derive the equation of a parabola given a focus and directrix.
  • Conics - Parabola
• CA.G.G.GPE.4Use coordinates to prove simple geometric theorems algebraically.
  • Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  • Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
  • Slope intercept form: y = mx + b
  • General form: Ax + By + C = 0
• CA.G.G.GPE.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
  • Parallel and perpendicular lines in linear functions
  • Parallel line equation
  • Perpendicular line equation
  • Combination of both parallel and perpendicular line equations
• CA.G.G.GPE.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
  • Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
• CA.G.G.GPE.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
  • Triangles
  • Rectangles
• CA.G.G.GMD.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
  • Circles and circumference
  • Surface area and volume of cylinders
  • Surface area and volume of cones
• CA.G.G.GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
  • Surface area and volume of pyramids
  • Surface area and volume of spheres
• CA.G.G.GMD.4Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
  • Surface area and volume of prisms
• CA.G.G.MG.3Apply geometric methods to solve design problems.
  • Word problems of polynomials
• CA.G.G.S.CP.1Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
  • Organizing outcomes
• CA.G.G.S.CP.2Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
  • Probability of independent events
• CA.G.G.S.MD.6(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
  • Introduction to probability
• CA.G.G.S.MD.7(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
  • Comparing experimental and theoretical probability