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Transcript
“Euclidean Geometry” – UNIT II: Polygons/Circles High School Mathematics “Geometry” published by HOLT, RINEHART, & WINSTON Target Time: 25-27 days ESSENTIAL STANDARD ESSENTIAL QUESTION DEPTH for MASTERY Sections #2—Uses algebraic skills and concepts to solve geometric problems throughout geometry What algebra skills and concepts are utilized in geometry? All Throughout unit #11—Classifies triangles as acute, right, obtuse, equilateral, isosceles, scalene; and classifies polygons as regular, convex, congruent What are the basic classifications of triangles and polygons? All 3.1 3.6 #14—States and applies the triangle sum, exterior angles, and polygon angle sum theorems How do you find the sum of the interior and exterior angles of any polygon? All 3.5 3.6 #19—States and applies properties of triangles and quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids What are the properties of triangles and quadrilaterals and how are they used? All 3.2 4.5 4.6 #21—Uses properties of quadrilaterals to establish and test relationships involving diagonals, angles, and lines of symmetry How do you use properties of quadrilaterals to establish relationships among diagonals, angles, and lines of symmetry? All 4.5 4.6 #26—States and applies the Pythagorean Theorem and its converse What are the applications of the Pythagorean Theorem and its converse? All 5.4 5.5 5.6 5.7 #27—States and applies properties of special right triangles, such as 45-45-90 and 30-60-90 triangles What are the properties of special right triangles and how are they used? All 5.5 COMMENTS Introduce area and perimeter Teach midsegment of trapezoid and median of trapezoid as synonymous terminology ESSENTIAL QUESTION DEPTH for MASTERY Sections COMMENTS How do you solve a right triangle using trigonometric functions? Without calculator or computer 10.1 10.2 Teach inverse sine and “arcsin” as synonymous terminology Save technology for enrichment unit How is trigonometry used in real world applications? Without calculator or computer 10.1 10.2 Teach inverse sine and “arcsin” as synonymous terminology Save technology for enrichment unit All 9.1 9.2 9.3 9.4 9.5 Introduce area and circumference How do you apply the relationships among circles, lines, segments, and the angles they form? All 9.1 9.2 9.3 9.4 9.5 IMPORTANT STANDARD ESSENTIAL QUESTION DEPTH for MASTERY Sections #1—Solves problems and practical applications using appropriate approaches and tools (including calculators and computers) and judges the reasonableness of results How do we solve problems and practical applications and judge the reasonableness of the results? All Throughout unit #20—Recognizes and applies the properties of inequalities to the measures of segments and angles in triangles How are inequalities related to segments and angles in triangles? All 5.4 4.8 ESSENTIAL STANDARD #28—Identifies and evaluates tangent, sine, and cosine ratios for an acute angle of a right triangle; uses a table, calculator, or computer to find the ratio for a given angle or find the angle for a given ratio #29—Uses the tangent, sine, and cosine ratios for right triangles to solve application problems such as indirect-measurement problems #30—Identifies and defines circles and their parts (center, arc, interior, exterior); segments and lines associated with circles (chord, diameter, radius, tangent, secant); properties of circles (congruent, concentric, tangent); relationship of polygons and circles (inscribed, circumscribed); angles (central; inscribed; formed by tangents, chords, and secants) #31—Applies geometric relationships to solving problems, such as relationships between lines and segments associated with circles, the angles they form, and the arcs they subtend; and the measures of these arcs, angles, and segments What are the parts of a circle and how are they related to other geometric figures? COMMENTS COMPACT STANDARD #16—Uses tools such as compass and straightedge, paper folding, tracing paper, mira, or computer to construct congruent segments, angles, triangles, and circles; an angle bisector; a perpendicular bisector; a perpendicular line from a point on a line; parallel lines; proportional segments; tangents; and inscribed and circumscribed polygons #48—Uses coordinate methods to explore, make conjectures, or prove properties of geometric figures, using tools such as algebra, graphing, and appropriate technology ESSENTIAL QUESTION DEPTH for MASTERY Sections What are the basic tools and construction methods used in geometry? OMIT proportional segments Throughout unit How can coordinate methods be used to explore geometry? All Supplement EOCT Domains Taught in this Unit: Polygons and Circles; Coordinate Geometry COMMENTS