Geometry
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Geometry CompetenciesDescription of Competency
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Mathematics
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Geometry CP
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Mathematical PracticesExplain and justify reasoning when solving mathematical problems.
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Mathematical Practices Indicator 1Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles
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Mathematical Practices Indicator 2Explain and use the relationship between the sine and cosine of complementary angles.
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Mathematical Practices Indicator 3Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
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Mathematical Practices Indicator 4Understand and apply the Law of Sine’s and the Law of Cosines to find unknown measurements in right and non-right triangles.
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Mathematical Practices Indicator 5Use Volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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Mathematical Practices Indicator 6Use Surface area formulas for cylinders, pyramids, cones, and spheres to solve problems.
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Mathematical Practices Indicator 7Define and apply properties of polygons.
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Number SystemsApply, prove, and extend properties of geometric figures.
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Number Systems Indicator 1Know precise definitions of angle, circles, perpendicular line, parallel line, and line segment, based on the undefined notations of point, line, distance along a line, and distance along a line, and distance around a circular arc.
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Number Systems Indicator 2Prove theorems about lines and Angles.
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Number Systems Indicator 3Prove theorems about triangles.
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Number Systems Indicator 4Prove theorems about parallelograms.
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Number Systems Indicator 5Determine lengths, arc and angles to solve problems with circles.
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Similarity & CongruenceConstruct and apply viable arguments about similarity and congruence.
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Similarity & Congruence Indicator 1Explain how and prove triangles similarity (AA, SSS, and SAS)
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Similarity & Congruence Indicator 2Explain how and prove triangle congruence (ASA, SAS, SSS, and HL)
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Similarity & Congruence Indicator 3Prove Theorems about triangles.
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Similarity & Congruence Indicator 4Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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Geometric RelationshipsDesign models that can be used to represent and understand geometric relationships.
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Geometric Relationships Indicator 1Use coordinates to prove simple geometric theorems algebraically.
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Geometric Relationships Indicator 2Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
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Geometric Relationships Indicator 3Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
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Geometric Relationships Indicator 4Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
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Geometric Relationships Indicator 5Use geometric shapes, their measures, and their properties to describe objects.
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Geometric Relationships Indicator 6Apply concepts of density based on area and volume in modeling situations
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Geometric Relationships Indicator 7Apply geometric methods to solve design problems.
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