## Geometry Essential Standards

**Geometry Essential Standards**

The High School Geometry courses provide a detailed study of the essential geometric strands outlined in the Common Core Learning Standards. The courses explore fundamental concepts algebraically, geometrically and graphically. The topics include Euclidean geometry, parallel lines, quadrilaterals, and coordinate geometry. Right triangles, right triangle trigonometry, constructions and locus theorems are also studied. The concepts of congruence and similarity are examined and the geometry of the circle is introduced. Proofs are emphasized in Euclidean and coordinate geometry. Through courses in Geometry students apply broad algebraic themes present in the Algebra I courses to discover, prove and construct geometric truths. The broad purpose of the courses in Geometry is to facilitate the development of reasoning through problem solving strategies and activities. The High School Geometry courses are leveled (Modified, Regular, and Honors) in order to differentiate student academic needs, but at their core all levels will be founded on the following essential standards:

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**Numbers & Quantity**

**N-Q.1.**Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

**Algebra**

**A-CED.1.**Create equations and inequalities in one variable and use them to solve problems.*Include equations arising from linear and quadratic functions, and simple rational and exponential functions.***A-REI.3.**Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.**A-REI.4.b.**Solve quadratic equations in one variable: Solve quadratic equations by inspection (e.g., for*x*2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

**Geometry**

**G.CO.1**. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.**G-CO.4.**Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.**G-CO.6.**Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.**G-CO.7.**Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.**G-CO.8.**Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.**G-CO.9.**Prove theorems about lines and angles.*Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.***G-CO.10.**Prove theorems about triangles.*Theorems include: 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.***G-CO.11.**Prove theorems about parallelograms.*Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.*

**G-CO.12.**Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).*Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.*

**G-SRT.2**. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.**G-SRT.3.**Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.**G-SRT.4.**Prove theorems about triangles.*Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.***G-SRT.5**. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.**G-SRT.6.**Understand 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.**G-SRT.8.**Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.**G-C.2.**Identify and describe relationships among inscribed angles, radii, and chords.*Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.***G-GPE.4.**Use coordinates to prove simple geometric theorems algebraically.*For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).***G-GPE.7.**Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

**G-GMD.3.** Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.