Harbor Creek School District. Advanced Geometry. Concepts Timeframe Skills Assessment Standards Undefined Terms Segments, Rays, and Distance

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1 Advanced Geometry Points, Lines and Planes Deductive Reasoning Concepts Timeframe Skills Standards Undefined Terms Segments, Rays, and Distance Angles Postulates and Theorems If Then Statements Converses Algebra Properties Proving Theorems Angles Perpendicular Lines Planning Proofs Quarter 1 E Identify and name points, lines and planes. E Name intersections of points, lines and planes. E Determine the measure of line segments using the coordinates. E Determine the measure of angles using the protractor. E Identify the sides and vertices of angles. E Recite the postulates and theorems which explain point, line and plane relationships. E Apply postulates and theorems to descriptive situations with points, lines and planes. E Recognize the hypothesis and conclusion of an If/Then statement. E Write the converse of an If/Then statement. E Find a counterexample to disprove an If/Then statement. E Demonstrate the use of if and only if statements. E Apply algebraic and congruence properties to proofs. E Write the Midpoint Theorem and Angle Bisector Theorem. E State all the various kinds of reasons that can be used in proofs. E Apply the definitions of complementary, supplementary, vertical angles, and perpendicular lines to find missing angle measures. E Plan proofs in two column form. Geometry Advanced Page 1

2 Logic Parallel Lines and Planes Concepts Timeframe Skills Standards Statements and Truth Tables Truth Tables for Conditionals Rules of Replacement Valid Arguments and Mistaken Premises Rules of Inference Application of Logic to Circuits Definitions of parallel and skew lines, parallel planes, and parallel lines and planes Transversals, Alternate Interior Angles, Same Side Interior Angles, and Corresponding Angles Parallel Line Properties Proving Lines are Parallel Triangle Angle Sum Polygon Angle Relationships Inductive vs. Deductive Reasoning Quarter 1 E Define compound statements. E Distinguish between conjunctions and disjunctions. E Symbolize written statements. E Write statements from logic symbols. E Set up truth tables for compound statements. E Create truth tables for conditional statements. E Evaluate truth tables for various combinations of statements. E Use rules of inference and/or rules of replacement to prove logical statements. E Sketch electrical circuits using symbolic logic statements. E Distinguish between intersecting, parallel and skew lines. E Identify types of special pairs of angles. E Apply parallel line theorems to determine the measures of all of the angles. E Apply angle relationships to determine if two lines are parallel. E Identify the classification of a triangle using sides and angles. E Find missing angle measures in triangles and other convex polygons by applying interior and exterior angle theorems. E Verbally compare and contrast deductive and inductive reasoning. Geometry Advanced Page 2

3 Congruent Figures Quadrilaterals Concepts Timeframe Skills Standards Congruent Polygons Prove Congruent by Three Methods Use Congruent to Prove Other Figures Congruent Isosceles Triangle Theorems Properties of Medians, Altitudes, and Perpendicular Bisectors Circumcenters and Incenters of Properties of Parallelograms Proving Quadrilaterals are Parallelograms Parallel Line Theorems Qualities of Special Parallelograms Trapezoid Properties Quarter 2 E Identify corresponding parts of congruent polygons. E Identify congruent triangles using SSS, SAS, ASA, AAS and HL. E State the meaning of CPCTC. E Prove figures congruent, after finding pairs of congruent triangles. E Identify properties of medians, altitudes and perpendicular bisectors. E Find the circumcenters and incenters of triangles. E Apply the definition of, and theorems for a parallelogram. E Prove quadrilaterals are parallelograms. E Apply midpoint theorems for triangles. E Identify the special relationships for the rectangle, rhombus and square. E Use parallelogram characteristics to determine if the shape is a rectangle, rhombus or square. E Define the trapezoid, isosceles trapezoid and the median of a trapezoid. Geometry Advanced Page 3

4 Inequalities in Geometry Similar Polygons Concepts Timeframe Skills Standards Inequalities Inverses and Contrapositives Equivalent Statements Indirect Proof Inequalities in One and Two Triangle Ratio and Proportion Properties of Proportion Similar Polygons Postulates for Similar Theorems for Similar Proportional Lengths Quarter 2 E Apply the properties of inequality to lengths of segments and measures of angles. E Use the exterior angle inequality theorem to find angle measures in triangles. E Write the contrapositive and inverse of a conditional statement. E State the pairs of logically equivalent statements. E Write an indirect proof in paragraph form. E Apply the inequality theorems for one and two triangles. E Express a ratio in simplest form. E Solve a proportion using the means/extremes property. E Rewrite proportions in equivalent forms. E Apply the properties of similar proportions. E State pairs of congruent angles and proportional sides when given a triangle similarity statement. E Apply the AA, SAS and SSS rules to state pairs of similar triangles. E Find correct proportions for triangles with the triangle proportionality theorem and the triangle angle bisector theorem. Geometry Advanced Page 4

5 Right Circles Concepts Timeframe Skills Standards Similarity in Right Pythagorean Theorem and its Converse Special Right The Tangent Ratio The Sine and Cosine Ratio Applications with Sine, Cosine and Tangent Ratios Basic terms for circles and spheres Tangent Lines Arcs and Central Angles Arcs and Chords Other Angles in Lengths of Segments of Circles Quarter 3 E Determine the geometric mean between two numbers. E Find missing lengths using the geometric mean as it applies to a right triangle with an altitude drawn to the hypotenuse. E Compute missing side lengths for a right triangle with the Pythagorean theorem. E Test triangle side lengths to determine whether the shape is an obtuse, acute or right triangle. E Apply the known relationships for a triangle and a triangle to find side lengths. E Recite the shortcut for sine, cosine and tangent ratios. E Calculate missing side and angle measures by using sine, cosine and tangent ratios. E Choose the correct function to solve application problems with right triangles. E Define a circle and sphere and other circle terms. E Sketch inscribed polygons, inscribed circles, circumscribed circles and circumscribed polygons. E Find missing segments using theorems of tangents and radii. E Find angle measures and arc lengths using theorems of arc and central angle relationships. E State and use the chord, arc, secant and radii theorems. E Solve problems using the central angle, inscribed angle, vertex in the circle and vertex out of the circle theorems. E Calculate missing lengths on chords, secant segments and tangent segments using these theorems. Geometry Advanced Page 5

6 Areas of Plane Figures Areas and Volumes of Solids Concepts Timeframe Skills Standards Areas of Rectangles Areas of Parallelograms, and Rhombuses Areas of Trapezoids Areas of Regular Polygons Circumferences and Areas of Circles Arc Lengths and Areas of Sectors Ratios of Areas Geometric Probability of Prisms of Pyramids of Cylinders and Cones of Spheres of Similar Solids Quarter 3 E Compute areas of rectangular regions using the rectangle area formula. E Calculate areas of parallelograms, triangles and rhombuses. E State and explain the formula for finding the area of a trapezoid. E Find the areas of regular polygons using the area formula. E Compute circumferences and areas of circles using the correct formulas. E Find arc lengths and sector areas by adjusting the formula to reflect the size of the circle indicated. E Find the ratios of areas by squaring the ratios of the sides or radii. E Write ratios to represent the probability of the occurrence of an event involving geometric figures. E Identify the parts of prisms and pyramids. E Calculate lateral areas, total areas, and volumes of right regular polygonal prisms and pyramids. E Compute lateral areas, total areas and volumes of right cylinders and right cones. E Find the area and volume of a sphere. E Apply the properties of similar solids to find missing dimensions. M11.E.3 M11.E.4 Geometry Advanced Page 6

7 Coordinate Geometry Concepts Timeframe Skills Standards The Distance Formula Circle and Radius Slope of a Line Parallel and Perpendicular Lines Vectors The Midpoint Formula Slope and y Intercept Graphing Linear Equations Writing Linear Equations Organizing and Solving Coordinate Geometry Proofs Quarter 4 E Apply the distance formula to a pair of coordinates to find the segment length. E Write the equation of a circle given the center point and radius. E Find the center point and radius of a circle when given the equation. E Apply the slope formula when given two coordinates. E State whether two lines are parallel, perpendicular or neither. E Write the vector and magnitude when given the two coordinates. E Find the midpoint coordinate of a segment. E Find the slope and y intercept of a line when given the equation of the line. E Sketch the graph of a line when given the equation. E Solve systems of linear equations by graphing, substitution, or elimination methods. E Write equations of lines from coordinates of points on the line and/or a slope for the line. E Provide general positions for the coordinates of the vertices of polygons and use them to prove geometric statements. M11.C.3 Geometry Advanced Page 7

8 Concepts Timeframe Skills Standards Mappings and Functions E Define the terms used in geometric mapping. Transformations Reflections Translations and Glide Reflections Rotations Dilations Composites of Mappings Inverses and the Identity Symmetry in the Plane and in Space Quarter 4 E Locate images by reflection. E Locate images by translation paired with reflection. E Locate images by rotation. E Locate images by dilation. E Locate images by composites of mappings. E Apply the identity and inverse of mappings to composite statements. E Identify figures that possess the qualities of symmetry. M11.C.2 M11.C.3 Geometry Advanced Page 8