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Transcript

GRADE LEVEL: HIGH SCHOOL GRADING PERIOD: QUARTER 2 CONTENT STANDARD INDICATORS LOGIC AND PROOFS G.LP.4: Develop geometric proofs, Proofs including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two‐column, paragraphs, and flow charts formats. G.PL.4: Know that parallel lines have Slope Equations of lines the same slope and perpendicular lines have opposite reciprocal slopes. Determine if a pair of lines are parallel, perpendicular, or neither by comparing the slopes in coordinate graphs and in equations. Find the equation of a line, passing through a given point, that is parallel or perpendicular to a given line. SUBJECT: GEOMETRY MASTER COPY 10‐8‐15 DATE: 2015‐2016 SKILLS ASSESSMENT VOCABULARY Proof Indirect proof Coordinate proofs Slope Equation of lines Develop and explain two‐ column proofs, flow chart proofs and paragraph proofs. Develop and explain proofs involving coordinate geometry. Determine if two lines are parallel, perpendicular or neither comparing slopes in coordinate graphs and in equations. Write equations of lines parallel or perpendicular to a given line. 1 Quiz Test Student Presentations Quiz Test CONTENT TRIANGLES Theorems of Triangles STANDARD INDICATORS SKILLS ASSESSMENT VOCABULARY G.T.1: Prove and apply theorems about triangles, including the following: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point; a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse Triangle congruence G.T.2: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Congruent triangle G.T.3: Explain and justify the process used to construct congruent triangles constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Classify triangles by sides and angles. Prove and apply triangle sum theorem. Prove and apply isosceles triangle theorems. Prove and apply the triangle mid‐segment theorem. Prove and apply properties of isosceles triangles. Prove and apply the Pythagorean Theorem. Prove and apply the third angle theorem. Prove and apply exterior angle theorem. Identify and prove triangle congruence by SSS, SAS, ASA, AAS and HL. Construct congruent triangles with a variety of geometric tools. Construct points of concurrency of triangles. Explain the process of these constructions. 2 Graphic Organizers Quiz Test Teacher Observation Quiz Test Class Presentations Geometer Sketchpad Activity Discovery Activity Quiz Test Equilateral Isosceles Scalene Acute Right Obtuse Triangle Sum Centroid SSS ASA SAS AAS HL Circumcenter Incenter Orthocenter Altitude CONTENT TRIANGLES Properties of congruent triangles STANDARD INDICATORS SKILLS ASSESSMENT VOCABULARY G.T.5: Use properties of congruent and similar triangles to solve real‐ world and mathematical problems involving sides, perimeters, and areas of triangles. Triangle Inequality G.T.6: Prove and apply the inequality theorems, including the following: Theorems triangle inequality, inequality in one triangle, and the hinge theorem and its converse. G.T.8: Develop the distance formula Pythagorean using the Pythagorean Theorem Distance Formula Theorem. Find the lengths and Midpoint formula midpoints of line segments in one‐or two‐dimensional coordinate systems. Find measures of the sides of polygons in the coordinate plane; apply this technique to compute the perimeters and areas of polygons in real‐world and mathematical problems. Solve real‐world problems involving congruent triangles. Solve problems using CPCTC (corresponding parts of congruent triangles are congruent). Prove and apply triangle inequality theorem. Prove and apply inequality in one triangle. Prove and apply the hinge theorem. Solve real‐world problems involving perimeter and area using the Pythagorean Theorem. Develop the distance formula using the Pythagorean Theorem. Find the measures of the sides and the midpoints of the sides of a polygon on the coordinate plane. 3 Quiz Test Quiz Test Quiz Test Discovery Activity CPCTC Triangle inequality Inequality in one triangle theorem Hinge theorem Pythagorean theorem Mid‐point Distance formula CONTENT TRIANGLES Special right triangles STANDARD INDICATORS SKILLS ASSESSMENT VOCABULARY G.T.11: Use special right triangles (30° ‐ 60° and 45° ‐45°) to solve real‐ world and mathematical problems. Use multiple diagrams of special right triangles to find missing side lengths. Use special right triangles to solve real‐world problems. 4 Quiz Test 30o – 60o right triangles 45o – 45o right triangles