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Core Content and Skills
Math Geometry R
2008-2009
BOE Approved

Foundations For Geometry  Content   Skills  Understanding points, lines, and planes Measuring and constructing segments Measuring and constructing angles Angle pairs Using formulas in geometry Midpoint and distance in the coordinate plane Transformations in the coordinate plane   Identify, Name, and Draw points, lines, planes, segments, and rays Construct and use midpoints of segments and congruent segments Name, classify, measure, and construct angles and angle bisectors Identify adjacent, vertical, complementary, and supplementary angles Apply formulas for perimeter, area, and circumference Develop and apply midpoint and distance formulas and the Pythagorean Theorem Identify and graph reflections, rotations, and translations     Geometric Reasoning  Content   Skills  Using inductive reasoning to make conjetures Conditional statements Using deductive reasoning to verify conjectures Bi-conditional statements and definitions Algebraic Proof Geometric Proof Flowcharts and paragraph proofs   Use inductive reasoning to identify patterns and make conjectures; find counterexamples to disprove conjectures Identify, write, and analyze truth values of conditional statements Write the converse, inverse, and contrapositive of a conditional statement Apply the Law of Detachment and the Law of Syllogism in logical reasoning Write and analyze bi-conditional statements Review properties of equality to write algebraic proofs Identify properties of equality and congruence Prove geometric theorems using deductive reasoning and writing two-column proofs Prove geometric theorems using deductive reasoning and writing flowchart proofs

Parallel and Perpendicular Lines  Content   Skills  Lines and angles Angles formed by parallel lines and transversals Proving lines parallel Perpendicular lines Slopes of lines Lines in the coordinate plane   Identify parallel, perpendicular, and skew lines Identify angles formed by two lines and a transversal Prove and use theorems about angles formed by parallel lines and a transversal Use angles formed by a transversal to prove two lines are parallel Prove and apply theorems about perpendicular lines Find the slope of a line Use slopes to identify parallel and perpendicular lines Graph lines and write their equations in slope-intercept and point-slope form Classify lines as parallel, intersecting, or coinciding

Triangle Congruence  Content   Skills  Classifying triangles Angle Relationships in a triangle Congruent triangles Triangle Congruence:  SSS and SAS Triangle Congruence:  ASA, AAS, and HL Triangle Congruence:  CPCTC Introduction to coordinate proof Isosceles and equilateral triangles   Classify triangles by their angle measures and side lengths Use triangle classification to find angle measures and side lengths Find the measures of the interior and exterior angles of triangles Apply theorems about the interior and exterior angles of triangles Use properties of congruent triangles Prove triangles congruent by using the definition of congruence Apply SAS and SSS to construct triangles and solve problems Prove triangles congruent by using SAS and SSS Apply ASA, AAS, and HL to construct triangles and solve problems Prove triangles congruent by using ASA, AAS, and HL Use CPCTC to prove parts of triangles are congruent Position figures in the coordinate plane for use in coordinate proofs Prove geometric concepts by using coordinate proof Prove theorems about isosceles and equilateral triangles Apply properties of isosceles and equilateral triangles

Properties and Attributes of Triangles  Content   Skills  Perpendicular and angle bisectors Bisectors of triangles Medians and altitudes of triangles The triangle midsegment theorem Indirect proofs and inequalities in one triangle Inequalities in two triangles The Pythagorean Theorem Applying special right triangles   Prove and apply theorems about perpendicular bisectors Prove and apply theorems about angle bisectors Prove and apply properties of perpendicular bisectors of a triangle Prove and apply properties of angle bisectors of a triangle Apply properties of medians of a triangle Apply properties of altitudes of a triangle Prove and use properties of triangle midsegments Write indirect profs Apply inequalities in one triangle Apply inequalities in two triangles Use the Pythagorean Theorem and its converse to solve problems Use the Pythagorean Theorem to classify triangles Justify and apply properties of 45-45-90 and 30-60-90 triangles

Polygons and Quadrilaterals  Content   Skills  Properties and attributes of polygons Properties of parallelograms Conditions for parallelograms Properties of special parallelograms Properties of kites of trapezoids   Classify polygons based on their sides and angles FInd and use the measures of interior and exterior angles of polygons Prove and apply properties of parallelograms Use properties of parallelograms to solve problems Prove a given quadrilateral is a parallelogram Prove and apply properties of rectangles, rhombuses, and squares Use properties of rectangles, rhombuses, and squares to solve problems Prove a given quadrilateral is a rectangle, rhombus, or square Use properties of kites and trapezoids to solve problems

Similarity  Content   Skills  Ratio and proportion Ratios in similar polygons Triangle similarity:  AA, SSS, and SAS Applying properties of similar triangles Using proportional relationships Dilations and similarity in the coordinate plane Similarity in right triangles   Write and simplify ratios Use proportions to solve problems Identify similar polygons Apply properties of similar polygons to solve problems Prove certain triangles are similar by using AA, SSS, and SAS Use triangle similarity to solve problems Use properties of similar triangles to find segment lengths Apply proportionality and triangle angle bisector theorems Use ratios to make indirect measurements Use scale drawings to solve problems Apply similarity properties in the coordinate plane Use the geometric mean to find segment lengths in right triangles Apply similarity relationships in right triangles to solve problems

Spatial Reasoning  Content   Skills  Developing formulas for regular polygons Perimeter and area in the coordinate plane Effects on changing dimensions proportionally Solid Geometry Representation of three dimensional figures Formulas in three dimensions Surface areas of prisms and cylinders Surface area of pyramids and cones Volume of prisms and cylinders Volume of pyramids and cones Spheres   Develop and apply the formula for the area of a regular polygon Find the perimeter and area of figures in the coordinate plane Describe the effect on perimeter and area when one or more dimensions of a figure are changed Apply the relationship between perimeter and area in problem solving Classify three-dimensional figures according to their properties Use nets and cross sections to analyze three-dimensional figures Draw representations of three-dimensional figures Recognize a three-dimensional figure from a given representation Apply Euler's formula to find the number of faces, edges, and vertices of a polyhedron Develop and apply the midpoint and distance formulas in three dimensions Learn and apply the formula for the surface area of a prism, cylinder, pyramid, cone, and sphere Learn and apply the formula for the volume of a prism, cylinder, pyramid, cone, and sphere

Circles  Content   Skills  Lines that intersect circles Arcs and chords Sector area and arc length Inscribed angles Angle relationships in circles Segment relationships in circles Circles in the coordinate plane   Identify tangents, secants, and chords Use properties of tangents to solve problems Apply properties of arcs and chords Find the area of sectors Find arc lengths Find the measure of an inscribed angle Use inscribed angles and their properties to solve problems Find the measures of angles formed by lines that intersect circles Use angle measures to solve problems Find the length of segments formed by lines that intersect circles Use the lengths of segments in circles to solve problems Write equations and graph circles in the coordinate plane Use the equation and graph of a circle to solve problems     Locus  Content   Skills  Simple Locus Compound locus   Identify 5 simple types of locus Find the locus of points given more than one object Determine points of intersection of two conditions Real-world applications of loci

Transformational Geometry  Content   Skills  Reflections Translations Rotations Compositions of transformations Symmetry Tessellations Dilations   Identify and draw reflections Identify and draw translations Identify and draw rotations Apply theorems about isometries Identify and draw compositions of transformations, such as glide reflections Identify and describe symmetry in geometric figures Use transformations to draw tessellations Identify regular and semiregular tessellations and figures that will tessellate Identify and draw dilations

Content   Skills