• 
  • 
• 
  • 
• 
  • 
• 
  • 
• 
  • 
• 
  • 
• 
  • 

Core Content and Skills
Math Geometry R
2007-2008
BOE Approved

Intro to Geometry  Content   Skills  Geometry Vocabulary   Recognizing and defining key words in vocabulary   Supplementary and Complementary Angles   Finding the complement and supplement of a given angle   Parallel lines cut by a transversal   Identifying and finding the measure of alternate interior, alternate exterior, and corresponding angles and identifying angles that are supplementary or congruent   Properties and angles of a triangle   Identify types of triangles, by sides and angles Identify and find angles of isosceles triangles Finding interior and exterior angles (exterior angle theorem) of a triangle   Sum of interior and exterior angles of a polygon   Finding the sum of the exterior angles of a polygon, finding the measure of each exterior angle of a regular polygon Finding the sum of the angles in a polygon, finding the measure of each angle of a regular polygon   Triangle Inequalities   Recognizing whether any 3 numbers can form the sides of a triangle. Given 2 integers, finding all possible values that could be 3rd side     Perimeter and Area  Content   Skills  Ratio of perimter and area of similar polygons   Finding the lengths of sides of similar polygons using the measures of the sides Finding the length of a side, or the perimeter, of similar polygons using one side of each polygon and the perimeter of one of the polygons Finding the length of a side of a polygon using one side of each polygon and the area of one of the polygons     Quadrilaterals  Content   Skills  Properties of quadrilaterals Properties of parallelograms Special Parallelograms, including rectangles, rhombuses, and squares Properties of trapezoids including isosceles trapezoids   Finding the measure of angles, sides and diagonals of a parallelogram Finding the measures of sides, angles, medians, and diagonals of a trapezoid Identifying properties of parallelograms and isosceles trapezoids

Area  Content   Skills  Finding area of polygons   FInd area of a polygon using formulas Find the area of a shaded region/circumscribed polygons Find area of shaded region of circumscribed polygons Find area of an irregular polygon - box in method     Quadratics  Content   Skills  Factoring Review Solving a quadratic equation by factoring Solve a quadratic equation by using the quadratic formula Graphing a quadratic equation Quadratic Transformations   Factoring a quadratic by using the GCF, trinomial, perfect square methods Factoring an expression completely Solving a quadratic equation by using the various factoring techniques Solving a quadratic equation by using the quadratic formula Identifying the nature of the roots after an equation is solved by the quadratic formula Graphing a quadratic equation - by hand and by the use of the graphing calculator Identifying the roots, the axis of symmetry, the minimum and maximum points of a quadratic equation Solving Quadratic Word Problems - ball toss, path of a rocket, etc. Recognizing what makes a parabola shift up, down, left, right ( use of graphing calculator)     Transformational Geometry  Content   Skills  Line Reflections Line Symmetry Point Reflection Point Symmetry Rotational Symmetry Translations Rotations Dilations Compositions Glide Reflections Coordinate Geometry Transformations of Polygons Isometries and Orientations   Identifying shapes that have line and point symmetry Reflecting a point of shape over the axes, over y=x, y=-x, x=k, y=k Sliding a point, or shape, given a specific translation Identifying a translation by looking at a graph or the new set of points Rotating a figure 90, 180, 270 and 360 degrees Identifying and graphing new points after a specific dilation Identifying and graphing a point, or figure, after a series of transformations Finding the area of a polygon after a transformation Identifying whether a shape remains the same size or is oriented in the same direction after a transformation     Volume  Content   Skills  Volume of circular solids Volume of cubes   Finding the volume of cylinders, cones and spheres Finding the volume of a cube and pyramid

Equations of a circle  Content   Skills  Graphing Circles Identify radius and center of a circle   Graph a circle on a coordinate plane, given an equation Identify the center and radius of a circle, given a graph or an equation Graph and make observations of a circle, given a word problem     Systems of Equations  Content   Skills  Solving systems of equations algebraically Solving systems of equations graphically   Review solving two linear systems algebriacally Review word problems involving two linear systems of equations Solve a linear-quadratic system of equations algebraically Review solving two linear systems of equations graphically Solve a linear-quadratic system of equations graphically Solve a linear-circle system of equations graphically Solve a quadratic-circle system of equations graphically

Constructions  Content   Skills  Constructing angles, segments, points through lines Constructions with triangles   Construcing congruent segments Bisecting a segment Creating congruent angles Bisecting a given angle Creating a perpendicular line through a point on the line and a point not on the line Constructing altitudes, medians and equilateral triangles     Locus  Content   Skills  Vocabulary Simple Locus Compound locus Locus and Coordinate Geometry   Identify the types of locus Draw a given locus using its description Finding compound loci Solving locus word problems - fence, treasure chest, trees, etc. Finding the points that satisfy a given condition in the coordinate plane ( equidistant from a line, a point, two lines, two points, etc )

Logic  Content   Skills  Terminology Statements Logical Reasoning Venn Diagrams   Negation, conjunction, disjunction, truth value Identifying Converse, Inverse, Contrapositive and Logically Equivalent statements Solving verbal problems using a Venn Diagrams     Identity Tables  Content   Skills  Identity and Inverse Element   Identifying identity and inverse element in an identity/binary table     Probability  Content   Skills  Empirical/Theoretical Probability Counting Principle Probability of 2 events ( and/or ) Permutations Combinations   Review empirical and theoretical probability Review probability of A and B, A or B Review Counting Principle, Permutations, probability with permutations Solving problems involving combinations Understanding the differences of combinations and permutations Solving probability problems involving combinations

Statistics  Content   Skills  Measures of Central Tendency   Identify mean, median, mode, and standard variation from data.   The Summation Symbol   Evaluate sums using proper summation notation.   Measures of Dispersion Grouped Data Normal Distribution   Use normal distribution to evaluate statistics.     Regression and Best Fit  Content   Skills  Exponential curve and regression   Identlfy which function would be the best fit given a set of data   Linear Regression   Creating a scatter plot Creating a linear equation to fit a set of data Identify practical significance of slope, y-intercept, ordered pair of a linear model Make predictions for future, given a set of data, by using linear model   Quadratic Regression   Create a "best fit" quadratic equation given a set of data Extrapolate information from given data to make predictions

Coordinate Geometry  Content   Skills  Slope, Midpoint and Distance formulas   Finding the slope of a line when given 2 points on the line Finding the midpoint of 2 given points; finding an endpoint, given one endpoint and a midpoint Finding the distance between 2 given points on a coordinate plane   Properties of quadrilaterals   Identify and apply properties of quadrilaterals   Coordinate Geometry Proofs   Proving a quadrilateral is a parallelogram Identify literal coordinates of a quadrilateral Proving that a quadrilateral is a rectangle, rhombus or a square Proving that a quadrilateral is a trapezoid (or an isosceles trapezoid) Create a polygon using literal coordinates General coordinate proofs     Euclidean Geometry  Content   Skills  Congruent triangles   Proving triangles congruent by SAS, ASA,SSS, AAS, HL   Euclidean Geometry Proofs   Proving a segment has a special property (median, angle bisector, perpendicular side) Proving a triangle is isosceles Proving parts of a triangle are congruent (CPCTC) Writing indirect proofs

Euclidean Geometry (cont'd)  Content   Skills  Geometry Inequalites   Applying triangle inequalities Writing proofs using geometry inequalities     Right Triangle and Proportions  Content   Skills  Right triangle similarity   Solving for a missing side of a right triangle using right triangle proportions Prove two triangles are similar (AA Theorem)   Special Right Triangles   Proving the Pythagorean Theorem Solving for sides of a right triangle using the 30-60-90 and 45-45-90 special right triangle rules

Geometry of the Circle  Content   Skills  Arcs and Angles Angles formed by Tangents, Secants, and Chords Inscribed Angles   Be able to relate angles and arcs following theorems.   Chords Measures of Chords, Tangent Segments, and Secant Segments Tangents and Secants   Be able to find additional parts of a circle using given parts Be able to use theorems to find the lengths of the measures of secants, tangents, and chords