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Arkansas: Geometry Mathematics Standards Math Standards

52 standards · 7 domains

STUDENTS WILL APPLY GEOMETRIC CONCEPTS TO REAL-WORLD SCENARIOS.

G.5.TM.1 Identify various geometric figures in order to identify what formulas are needed to solve situational problems (e.g., decompose and rearrange geometric figures)
G.5.TM.2 Compute measurements of geometric figures such as area, surface area (including area of sectors), volume, perimeter, and circumference (including arc length) for real-world scenarios
G.5.TM.3 Use trigonometric ratios (e.g., sine, cosine, tangent) to calculate angles and lengths of sides in real-world scenarios
G.5.TM.4 Analyze how changing dimensions will affect the perimeter, circumference, area, surface area, or volume in real-world scenarios
G.5.TM.5 Determine the role angles play in a situational problem (e.g., structural strength and stability, angle straps for lifting, angles used to cut hair)
G.5.TM.6 Apply right-triangle relationships using Pythagorean Theorem, special right triangles, and trigonometry in real-world scenarios (e.g., roof construction, building the frame of a car, calculating machined parts)
G.5.TM.7 Draw and interpret with or without the use of technology (e.g., house plans, engineering drawings, fashion design)
G.5.TM.8 Use cross-sections of three-dimensional shapes to relate to two-dimensional figures
G.5.TM.9 Describe the transformation of polygons in the coordinate plane as they relate to real-world scenarios (e.g., cookie cutting, fabric cutting, machine dies)

CIRCLES

G.CIR.1 Apply the precise definition and standard geometric notation for a circle to understand geometric relationships.
G.CIR.2 Recognize and apply relationships between angles, radii, and chords, tangents, and secants including:
G.CIR.3 Use the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems.
G.CIR.4 Use the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems.
G.CIR.5 Explain why the formulas for the area and circumference of a circle work using dissection and informal limit arguments.
G.CIR.6 Write the equation of a circle, given the radius and center, where the center is at the origin or another point.
G.CIR.7 Identify the center and radius of a circle, given the equation of a circle, where the center is at the origin or another point.
G.CIR.8 Apply the equation of a circle to solve real-world problems.

GEOMETRIC FIGURES

G.GF.1 Find the volume and surface area of complex three-dimensional figures composed of prisms, pyramids, cones, cylinders, and spheres.
G.GF.2 Use three-dimensional geometric figures and their measures to model real-world objects and solve problems.
G.GF.3 Explain why the formulas for the volume and surface area of a cylinder, pyramid, and cone work.
G.GF.4 Apply the Pythagorean Theorem to determine missing measurements in a three-dimensional figure.
G.GF.5 Identify the three-dimensional figure generated by rotating a two-dimensional figure.
G.GF.6 Apply theorems about quadrilaterals, including those involving angles, diagonals, and sides to solve problems.
G.GF.7 Prove that a given quadrilateral is a parallelogram, rhombus, rectangle, square, kite, or trapezoid, and apply these relationships to solve problems.
G.GF.8 Prove and apply theorems about triangles including:
G.GF.9 Calculate the perimeter of polygons when given the vertices, including using the distance formula.
G.GF.10 Calculate the area of triangles and rectangles when given the vertices, including using the distance formula and decomposing figures.
G.GF.11 Describe reflectional and rotational symmetry as they apply to a rectangle, parallelogram, trapezoid, or regular polygon.
G.GF.12 Calculate probabilities as a proportion of area in a geometric context.

LINES & ANGLES

G.LA.1 Use precise definitions and standard geometric notation for angles, perpendicular lines, parallel lines, and line segments based on the undefined notions of point, line, and distance along a line.
G.LA.2 Make formal geometric constructions with a variety of tools and methods including:
G.LA.3 Determine the point that cuts a line segment into a specified ratio on a number line and a coordinate plane, including finding the midpoint.
G.LA.4 Derive the distance and midpoint formulas and use the formulas, including the slope formula, to verify geometric relationships on a coordinate plane.
G.LA.5 Prove and apply slope criteria of parallel and perpendicular lines to solve problems.
G.LA.6 Write an equation of a line that is parallel or perpendicular to a given line and passing through a given point.
G.LA.7 Prove and apply theorems about lines and angles including:

RIGHT TRIANGLES

G.RT.1 Apply the properties of special right triangles (30°-60°-90° and 45°-45°-90°) to solve real-world and mathematical problems.
G.RT.2 Prove and apply the Pythagorean Theorem and its converse.
G.RT.3 Explain how the definitions for trigonometric ratios are developed by similarity and how the side ratios in right triangles are properties of the angles in the triangle.
G.RT.4 Explain the relationship between the sine and cosine of complementary angles and use them to solve problems.
G.RT.5 Determine the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles.
G.RT.6 Use trigonometric ratios (sine, cosine, and tangent) to calculate missing side lengths and angle measures in a right triangle, including applications of angles of elevation and depression; include real-world and mathematical problems.

SIMILARITIES & CONGRUENCE

G.SC.1 Given two figures, apply the definition of similarity in terms of a dilation to identify similar figures, proportional sides, and corresponding congruent angles.
G.SC.2 Develop and apply the criteria of similarity for triangles (AA~, SAS~, and SSS~) to solve problems and prove geometric relationships.
G.SC.3 Use transformations to prove all circles are similar.
G.SC.4 Explain, using rigid motion transformations, why two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.SC.5 Develop and apply the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL) to solve problems and prove geometric relationships.

TRANSFORMATIONS

G.TRF.1 Describe rotations, reflections, and translations as functions that take points in the coordinate plane as inputs and give other points as outputs; write in prime notation.
G.TRF.2 Compare transformations that preserve distance and angle (rotations, reflections, and translations) to those that do not (dilations) to develop definitions for congruence and similarity.
G.TRF.3 Apply understanding of angles, circles, perpendicular lines, parallel lines, and line segments to develop definitions for rotations, reflections, and translations.
G.TRF.4 Use geometric constructions to represent rotations, reflections, translations, and dilations in the plane with a variety of tools and methods.
G.TRF.5 Given two congruent figures, identify the sequence of transformations that maps one figure to another.