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Transcript
Williston School District 29 Geometry Concepts Pacing Guide Chapter 1 Foundations of Geometry Focus Questions Overview Focus Indicators 90 Total Days Day 1 2 3 4 5 1-1, Understanding Points, lines, and Planes- Naming, Describing and Drawing 1-2. Measuring and Constructing Segments- Finding Lengths 1-3, Measuring and Constructing Angles- Classifying each Angle 1-4, Pairs of Angles- Classifying the Pairs 5days 1-5, Using Formulas to Find Area, Perimeter and Circumference 1-6,Finding Midpoint and Distance in the Coordinate Plane 1-7, Identify Transformations in Coordinate Plane 2-1, Using Inductive Reasoning to Make Conjectures 2-2, Identifying Conditional Statements 2-3, Deductive Reasoning to Verify Conjectures 2-4, Identifying Biconditional Statements and Definitions 2-5, Algebraic Proof writing Collinear and Coplanar Points and Postulates S is between R and T find RT, ; Segment Addition Postulate Ray KM bisects the Angle, find the Measure Finding Measures of complementary and Supplementary Angles Find Area, Perimeter and Circumference for Triangles, Rectangles, Squares, Parallelograms and Circles. Use the Midpoint and Distance formula to Length Reflections, Rotations, and Translations from given information. Completing Conjectures, and drawing Counterexamples “p” Then “q”, converse, Inverse, Contrapositive Law of Syllogism, and Law of Detachment Complete each statement to form a new Biconditional Identify Property that G.CO.1,2,4,5,12 A.REI.1, G.CO.9 2-6, Geometric Proof Writing 2-7, Writing Flow and Paragraph Proofs 3-1, Identify, Parallel, Skew, and Perpendicular lines 3-2, Identify Angles formed by Parallel lines and Transversals 3-3, Proving Lines Parallel 3-4, Identifying Perpendicular lines and their equations 3-5, Identifying the slopes of Parallel and Perpendicular Lines 4-1, Congruence and Transformations with Triangles 4-2, Classifying triangles 4-3, Identifying Congruent Triangles 4-4, Identifying Triangle Congruence Postulates 4-5, More Triangle Congruence Theorems 4-6, Identifying the converse of Congruence 4-7, Identifying Special Properties of Isosceles and Equilateral Triangles 5-1, Finding Different Measures given Perpendicular Bisectors and Angle Bisectors 5-2, Finding Special Relationships in Triangles with Concurrent Points justifies each statement Two-Column Proofs, writing justifications for each step. Use the given plan to write each of the following Proofs. From Given figure identify the following Finding Each Angle Measure with proper Theorem or Postulate. Use Given Information and theorems to show lines are Parallel Naming the shortest segment and writing an inequality Slope Formula, and Theorems to show relationships Reflections, Rotations, and Translations Isosceles, Equilateral, Scalene, and Obtuse, and Acute. Using the Definition of Congruent Triangles to find measures of corresponding parts SSS, and SAS Congruence Postulates in Proofs HL, ASA, and AAS in Geometric Proofs Corresponding Parts of Congruent Triangles are Congruent Finding different values using different Theorems ( Base Angles Theorem) Perpendicular bisector Theorem and Angle Bisector Theorems Circumcenters, Incenters, and Centroids with Medians and Altitudes of Triangles G.CO.1,9,12 G.GPE.5 G.CO.6,7,8,10 G.SRT.5 G.MG.3 G.GPE.4 G.CO.9,10 G.SRT.4,8 G.C.3 G.MG.3 5-3, Finding length of Midsegments of Triangles 5-4, Drawing Conclusions using Indirect proofs 5-5, Compare measures given inequalities in two triangles 5-6, Finding lengths using Pythagorean Theorem and Special Right Triangles 6-1, Properties and Attributes of polygons 6-2, Identifying Properties and Conditions for Paralellograms 6-3, Identifying properties and conditions of Special Parallelograms 6-4, Proving properties of Kites and Trapezoids 7-1, Finding Ratios in Similar Polygons 7-2, Defining the Similarity in the Transformation 7-3, Proving triangles Similar 7-4, Applying Properties of Similar triangles-finding Corresponding angles and Sides 8-1, Using Right triangle Similarity to find corresponding lengths 8-2, Using Trigonometric Ratios to solve Right Triangles 8-3, Using Angle of Elevation and Depression to solve right Triangles. 8-4, Finding lengths in triangles that are not right. 8-5, Calculating time and space using directed Line segments 12-1, Finding length of lines that intersect circles 12-2, Finding Length of Arcs and Chords 12-3,Finding sector area and Arclength 12-4, Finding Inscribed angles and segment relationships in Circles Midsegment Theorem Inequalities in One Triangle Hinge Theorem and Hinge Theorem Converse Square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs. 30-60-90, 45-45-90 right Triangles Based on number of sides and Convex or non-Convex Opposite sides, parallel and congruent. Opposite angles congruent, consecutive angles supplementary Rectangles, Rhombus, and Squares Giving the best name for the quadrilateral Define Similar Polygons Dilations AA, SSS, SAS, Similarity Postulates and Theorems Triangle Proportionality Theorem and Dilations Geometric Means G.CO.11,13 G.GPE.5 G.MG.3 G.SRT.1,2,3,4,5 G.CO.2 G.MG.3 G.SRT.6,7,10 G.SRT.11 Sin, Cos, and Tan Sin, Cos, and Tan Law of Sines and Law of Cosines Vectors, addition and multiplication Tangents, Secants, Chords, and Radii Central angles and Intercepted Arcs M/360*”PI” r^2 M/360*2*”PI” *r ½ measure of intercepted arc, Area of sector – Area of Triangle G.C.2,3,4,5 G.CO.13 G.GPE.1 Finding equations of Circles in the coordinate Plane Finding Surface Area and Volume of Geometric Solids 90 days (x-h)^2+(y-k)^2=r^2 Cones, Pyramids, Spheres, and Rectangular Solids G.GMD.1,3,4 G.MG.1,2,3