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The School District of Palm Beach County GEOMETRY REGULAR 2nd Quarter Scope 2010 - 2011 Benchmarks Topic & Suggested Pacing Next Generation Sunshine State Standards Use methods of direct and indirect proof and determine MA.912.D.6.4 whether a short proof is logically valid. 5.5 Find the lengths and midpoints of line segments in two- MA.912.G.1.1 dimensional coordinate systems. 5.1, 5.3 October 18 December 17 Congruent Figures Triangle Congruence by SSS and SAS Identify and describe convex, concave, regular, and irregular MA.912.G.2.1 polygons. 6.1 Triangle Congruence by ASA and AAS Determine the measures of interior and exterior angles of MA.912.G.2.2 polygons, justifying the method used. 6.1 Using Corresponding Parts of Congruent Triangles Use properties of congruent and similar polygons to solve MA.912.G.2.3 mathematical or real-world problems. 4.4 Isosceles and Equilateral Triangles Congruence in Right Triangles Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine Congruence in Overlapping congruence, similarity, and symmetry. Know that images Triangles MA.912.G.2.4 formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations Midsegments of of the plane using polygons. Triangles 4.1 Perpendicular Student Target I can… • Recognize congruent figures and their corresponding parts • Prove two triangles congruent using the SSS and SAS Postulates • Prove two triangles congruent using the ASA Postulate • Prove two triangles congruent using the AAS Theorem • Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent • Use and apply properties of isosceles and equilateral triangles • Prove right triangles congruent using the HypotenuseLeg Theorem • Identify congruent overlapping triangles • Prove two triangles congruent using other congruent triangles • Use properties of midsegments to solve problems • Use properties of perpendicular bisectors and angle bisectors • Identify properties of perpendicular bisectors • Identify properties of angle bisectors • Identify properties of medians and altitudes of a triangle • Identify the orthocenter of a triangle • Use indirect reasoning to write proofs • Use inequalities involving angles and sides of triangles • Apply inequalities in two triangles • Find the sum of the measures of the interior angles of a polygon Core Tutorial Support AYP Support Pearson Geometry 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5.1 5.2 5.3 5.4 5.5 5.6 5.7 6.1 6.2 6.3 6.4 6.5 6.6 Triangle Proofs (ASA, SAS, AAS, SSS, or HL) MA.912.G.1.1 MA.912.G.2.2 CPCTC Video MA.912.G.2.3 Congruent and Similar Triangle Video MA.912.G.2.4 Isosceles and Equilateral Triangles Video MA.912.G.3.4 Using Isoceles and Equilateral Triangles Video MA.912.G.4.6 Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, MA.912.G.3.1 parallelogram, trapezoid, and kite. 6.2-6.6 Compare and contrast special quadrilaterals on the basis of MA.912.G.3.2 their properties. 6.4-6.6 MA.912.G.3.4 Prove theorems involving quadrilaterals. 6.2-6.6 Classify, construct, and describe triangles that are right, acute, MA.912.G.4.1 obtuse, scalene, isosceles, equilateral, and equiangular. polygon • Find the sum of the measures of the exterior angles of a polygon • Use relationships among sides and angles of Bisectors in parallelograms Triangles • Use relationships among diagonals of parallelograms Medians and • Determine whether a quadrilateral is a parallelogram Altitudes • Define and classify special types of parallelograms Indirect Proof • Use properties of diagonals of rhombuses and rectangles • Determine whether a parallelogram is a rhombus or Inequalities in rectangle One Triangle • Verify and use properties of trapezoids • Verify and use properties of kites Perpendicular and Angle Bisectors Inequalities in Two Triangles 4.5 Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors,orthocenter, centroid, MA.912.G.4.2 incenter, and circumcenter. 5.2-5.4 MA.912.G.4.3 Construct triangles congruent to given triangles. 4.2-4.3 The Polygon Angle Sum Theorems Properties of Parallelograms Proving That a Quadrilateral Is a Parallelogram Use properties of congruent and similar triangles to solve MA.912.G.4.4 problems involving lengths and areas. 4.4 MA.912.G.4.5 Apply theorems involving segments divided proportionally. 5.1, 5.4, 6.2 Prove that triangles are congruent or similar and use the Properties of Rhombuses, Rectangles, and Squares Conditions for Rhombuses, Rectangles, and Squares MA.912.G.4.6 concept of corresponding parts of congruent triangles. 4.1-4.4, 4.6-4.7 Apply the inequality theorems: triangle inequality, inequality in MA.912.G.4.7 one triangle, and the Hinge Theorem. Trapezoids and Kites Overlapping Triangles Midsegment of a Triangle Video Lesson Angle Bisector Perpendicular and Angle Bisectors Video Bisector in Triangles Medians and Altitudes Video Lesson Indirect Proof Triangle Inequality Theorem and Inequalities for Two Triangles 5.6-5.7 MA.912.G.5.4 Solve real-world problems involving right triangles. 4.6 Angle Sum Theorem MA.912.G.4.7 MA.912.G.5.4 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a MA.912.G.8.5 variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs. 5.5, 6.2-6.3 The Properties of a Parallelogram Theorems Dealing with Parallelogram s The Types and Properties of Quadrilaterals Secondary Data-Driven Benchmark Comprehension Check