Growth: Geometry International (2017) Gizmos | Browse by Core Curriculum

1: Properties of Geometric Shapes

1.1: Points, Lines, Planes, and Angles

1.1.1: Geometric Constructions

1.1.1.1: [RIT 257 - 257] Identifies the geometric construction of an angle bisector

1.1.1.2: [RIT 263 - 263] Identifies the geometric construction of a line segment bisector or the midpoint of a line segment

1.1.2: Points, Lines, Segments, Rays, and Angles

1.1.2.1: [RIT 186 - 207] Identifies right angles

1.1.2.2: [RIT 193 - 196] Identifies parallel lines

1.1.2.3: [RIT 202 - 215] Identifies points, lines, rays, line segments, and angles

1.1.2.4: [RIT 202 - 209] Identifies acute or obtuse angles

1.1.2.5: [RIT 203 - 203] Knows the definition of an acute angle

1.1.2.6: [RIT 213 - 239] Identifies perpendicular lines involving real-world objects

1.1.2.7: [RIT 226 - 240] Knows the definition of an angle

1.1.2.8: [RIT 236 - 237] Identifies perpendicular lines

1.1.2.9: [RIT 248 - 248] Defines midpoints of line segments

1.1.2.10: [RIT 275 - 275] Defines bisectors of line segments

1.1.3: Angle Measurement

1.1.3.1: [RIT 187 - 239] Calculates unknown angle measures using the additive property of angles

1.1.3.2: [RIT 211 - 222] Measures non-right angles using a protractor

1.1.4: Relationships involving Lines, Angles, and Polygons

1.1.4.1: [RIT 215 - 258] Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles

1.1.4.2: [RIT 226 - 257] Solves problems involving parallel lines cut by a transversal

1.1.4.3: [RIT 240 - 240] Defines complementary and supplementary angles

1.1.4.4: [RIT 245 - 249] Identifies corresponding, alternate interior, and alternate exterior angles

1.1.4.5: [RIT 248 - 258] Identifies complementary and supplementary angles

1.1.4.6: [RIT 253 - 267] Determines the conditions necessary to show that two lines are parallel

1.1.4.7: [RIT 269 - 269] Identifies vertical angles

1.2: Polygons and Circles

1.2.1: Circles

1.2.1.1: [RIT 208 - 208] Knows the number of degrees in a circle

1.2.1.2: [RIT 218 - 231] Identifies radii and diameters of circles

1.2.1.3: [RIT 236 - 236] Recognizes the relationship between the diameter and the radius of a circle

1.2.1.5: [RIT 242 - 292] Uses properties of central and inscribed angles to solve problems involving circles

1.2.1.6: [RIT 243 - 271] Solves problems involving inscribed angles on a diameter

1.2.1.7: [RIT 250 - 263] Understands that the ratio between the circumference and the diameter of a circle is equal to pi

1.2.1.8: [RIT 256 - 271] Uses properties of chords to solve problems involving circles

1.2.1.11: [RIT 263 - 263] Recognizes a precise definition of circles

1.2.1.12: [RIT 263 - 274] Calculates arc lengths

1.2.1.14: [RIT 266 - 266] Solves problems involving arc measures of a circle

1.2.2: Identification and Classification of 2-D Shapes

1.2.2.1: [RIT 210 - 260] Knows properties of parallelograms, including special parallelograms such as squares, rhombuses, etc.

1.2.2.2: [RIT 213 - 245] Knows properties of special triangles, such as acute, right, scalene, etc.

1.2.3: Perimeter/Circumference

1.2.3.1: [RIT 250 - 250] Understands that the ratio between the circumference and the diameter of a circle is equal to pi

1.2.4: Relationships involving Lines, Angles, and Polygons

1.2.4.1: [RIT 194 - 194] Identifies diagonals of polygons

1.2.4.2: [RIT 220 - 250] Applies the formula for the sum of the interior angles of a polygon

1.2.4.3: [RIT 221 - 233] Applies the Triangle Angle-Sum Theorem to determine the measure of an unknown angle

1.2.4.4: [RIT 223 - 241] Recognizes that the sum of the interior angles of a triangle is 180 degrees

1.2.4.5: [RIT 228 - 250] Applies properties of isosceles triangles to determine the measure of an unknown angle

1.2.4.7: [RIT 237 - 268] Solves problems by applying multiple properties of angles, including interior and exterior angles of triangles; complementary, supplementary, and vertical angles; and angles created by perpendicular lines or parallel lines cut by a transversal

1.2.4.9: [RIT 240 - 240] Determines the number of diagonals that can be drawn from one vertex in a polygon

1.2.4.10: [RIT 241 - 276] Applies the Triangle Inequality Theorem

1.2.4.11: [RIT 242 - 242] Applies the Triangle Exterior Angle Theorem to determine the measure of an unknown angle

1.2.4.12: [RIT 256 - 258] Applies the formula for the measure of each exterior angle of a regular polygon

1.2.4.14: [RIT 269 - 269] Applies the formula for the measure of each interior angle of a regular polygon

1.3: Three-Dimensional Figures

1.3.1: Identification and Classification of 3-D Shapes

1.3.1.1: [RIT 191 - 223] Identifies faces, bases, edges, or vertices of 3-D shapes

1.3.1.2: [RIT 195 - 210] Describes cones, cylinders, and spheres based on the shape of surfaces and/or number of bases or vertices, without pictures given

1.3.1.5: [RIT 241 - 241] Identifies and names polyhedrons

1.3.2: Spatial Concepts and Symmetry

1.3.2.1: [RIT 175 - 208] Identifies multiple views of structures composed of cubes

1.3.2.2: [RIT 184 - 229] Identifies and creates nets for prisms

1.3.2.3: [RIT 186 - 202] Identifies and creates nets for pyramids

1.3.2.4: [RIT 190 - 241] Identifies and creates nets for cones

1.3.2.5: [RIT 209 - 249] Identifies single views of structures composed of cubes

1.3.2.6: [RIT 212 - 236] Identifies and creates nets for cylinders

1.3.2.7: [RIT 216 - 216] Identifies single views of 3-D shapes

1.3.2.8: [RIT 244 - 270] Identifies the cross-sections of 3-D shapes

2: Measurement of Geometric Shapes

2.1: Perimeter and Circumference

2.1.1: Perimeter/Circumference

2.1.1.1: [RIT 200 - 245] Solves problems involving perimeters of rectangles within a real-world or mathematical context

2.1.1.2: [RIT 209 - 230] Determines side lengths given the perimeter of rectangles

2.1.1.3: [RIT 213 - 239] Determines the circumference of circles, given the formula

2.1.1.4: [RIT 220 - 238] Solves problems involving decimals and perimeters of rectangles within a real-world or mathematical context

2.1.1.5: [RIT 222 - 251] Determines the circumference of circles, formula not provided

2.1.1.7: [RIT 231 - 231] Determines the ratio between perimeters of scaled figures

2.1.1.8: [RIT 232 - 240] Describes the effect on perimeter when dimensions of a non-rectangular polygon are changed

2.1.1.9: [RIT 233 - 244] Identifies the formula for the perimeter of a polygon

2.1.1.10: [RIT 248 - 248] Solves problems involving perimeters of non-rectangular polygons within a real-world or mathematical context

2.2: Area and Surface Area

2.2.1: Area

2.2.1.1: [RIT 200 - 222] Determines the area of rectangles with whole-number sides, given the formula

2.2.1.2: [RIT 201 - 224] Determines the area of rectangles with whole-number sides, formula not provided

2.2.1.3: [RIT 206 - 224] Determines side lengths given the area of rectangles

2.2.1.4: [RIT 206 - 226] Determines the area of figures composed of whole and partial unit squares

2.2.1.5: [RIT 209 - 238] Solves problems involving areas of rectangles within a real-world or mathematical context

2.2.1.6: [RIT 213 - 250] Determines the area of parallelograms, formula not provided

2.2.1.8: [RIT 223 - 245] Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context

2.2.1.9: [RIT 223 - 242] Determines the area of rectangles with decimal sides, formula not provided

2.2.1.10: [RIT 224 - 257] Describes the effect on area when dimensions of a rectangle are changed

2.2.1.11: [RIT 224 - 224] Determines the base or height given the area of a parallelogram

2.2.1.12: [RIT 224 - 252] Describes the effect on area when dimensions of a triangle are changed

2.2.1.14: [RIT 228 - 267] Solves problems involving areas of figures composed of polygons within a real-world or mathematical context

2.2.1.16: [RIT 230 - 235] Determines the area of triangles, given the formula

2.2.1.18: [RIT 232 - 232] Identifies the formula for the area of a circle

2.2.1.19: [RIT 234 - 239] Determines the area of circles, given the formula

2.2.1.20: [RIT 235 - 260] Determines the perimeter of rectangles given the area

2.2.1.21: [RIT 236 - 254] Determines the area of triangles, formula not provided

2.2.1.22: [RIT 236 - 260] Determines the area of figures composed of polygons

2.2.1.23: [RIT 237 - 250] Determines the area of rectangles given the perimeter

2.2.1.24: [RIT 240 - 269] Determines the ratio between areas of scaled figures

2.2.1.27: [RIT 244 - 260] Determines the circumference given the area of a circle

2.2.1.29: [RIT 247 - 247] Determines the radius or diameter given the area of a circle

2.2.1.30: [RIT 249 - 257] Determines the area of circles, formula not provided

2.2.1.31: [RIT 251 - 251] Determines the area of figures composed of polygons and circles

2.2.1.34: [RIT 260 - 270] Describes the effect on area when the radius or diameter of a circle is changed

2.2.1.35: [RIT 261 - 261] Describes the effect on area when the circumference of a circle is changed

2.2.1.36: [RIT 265 - 265] Solves problems involving areas of circles within a real-world or mathematical context

2.2.3: Surface Area

2.2.3.1: [RIT 236 - 248] Uses the net of a prism to solve surface area problems within a real-world or mathematical context

2.2.3.2: [RIT 238 - 261] Determines the surface area of rectangular prisms or cubes, formula not provided

2.2.3.4: [RIT 241 - 241] Determines the surface area of cylinders, given the formula

2.2.3.5: [RIT 241 - 248] Determines the surface area of a prism given a net

2.2.3.6: [RIT 246 - 246] Determines the surface area of cones, given the formula

2.2.3.7: [RIT 251 - 252] Determines the surface area of pyramids, given the formula

2.2.3.8: [RIT 252 - 252] Determines the surface area of triangular prisms, formula not provided

2.2.3.9: [RIT 252 - 256] Determines the surface area of pyramids, formula not provided

2.2.3.10: [RIT 255 - 263] Describes the effect on surface area when dimensions of a rectangular prism are changed

2.2.3.12: [RIT 260 - 263] Solves problems involving surface areas of prisms within a real-world or mathematical context

2.2.3.13: [RIT 266 - 269] Determines the surface area of cylinders, formula not provided

2.2.4: Perimeter/Circumference

2.2.4.1: [RIT 244 - 244] Determines the circumference given the area of a circle

2.2.5: Problem Solving with Units

2.2.5.1: [RIT 265 - 265] Solves problems involving areas of circles within a real-world or mathematical context

2.3: Volume

2.3.1: Conversion of Units

2.3.1.1: [RIT 282 - 282] Converts units of volume within the same measurement system

2.3.2: Volume

2.3.2.1: [RIT 206 - 229] Determines the volume of rectangular prisms, given the formula

2.3.2.2: [RIT 206 - 225] Determines the volume of figures by counting unit cubes

2.3.2.3: [RIT 207 - 241] Determines the volume of rectangular prisms, formula not provided

2.3.2.4: [RIT 218 - 218] Solves problems involving rectangular prisms composed of unit cubes

2.3.2.5: [RIT 220 - 264] Solves problems involving volumes of rectangular prisms within a real-world or mathematical context

2.3.2.6: [RIT 226 - 226] Identifies the formula for the volume of a rectangular prism

2.3.2.7: [RIT 227 - 244] Identifies units for measuring volume

2.3.2.9: [RIT 231 - 253] Determines the volume of figures composed of rectangular prisms

2.3.2.11: [RIT 235 - 268] Determines the volume of pyramids, given the formula

2.3.2.12: [RIT 237 - 240] Determines the volume of cylinders, given the formula

2.3.2.13: [RIT 239 - 273] Describes the effect on volume when dimensions of a rectangular prism are changed

2.3.2.15: [RIT 245 - 245] Determines the volume of spheres, given the formula

2.3.2.16: [RIT 250 - 275] Determines the volume of cylinders, formula not provided

2.3.2.19: [RIT 254 - 274] Determines the volume of pyramids, formula not provided

2.3.2.21: [RIT 258 - 258] Determines the radius or diameter of a cylinder given the volume and height

2.3.2.26: [RIT 266 - 266] Solves problems involving volumes of 3-D figures composed of cones, cylinders, and spheres within a real-world or mathematical context

2.3.2.27: [RIT 266 - 266] Determines the volume of figures composed of rectangular and triangular prisms

2.3.2.29: [RIT 269 - 281] Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height

2.3.2.30: [RIT 270 - 270] Determines the volume of spheres, formula not provided

2.3.2.31: [RIT 273 - 273] Determines the volume of cones, formula not provided

2.3.2.32: [RIT 276 - 276] Solves problems involving volumes of cones within a real-world or mathematical context

2.3.2.33: [RIT 278 - 278] Solves problems involving volumes of cylinders within a real-world or mathematical context

3: Geometric Relationships

3.1: Congruence and Similarity

3.1.1: Congruence

3.1.1.1: [RIT 184 - 184] Identifies congruent shapes, given informal language

3.1.1.2: [RIT 186 - 230] Identifies congruent shapes, given formal language

3.1.1.3: [RIT 194 - 206] Identifies corresponding sides and angles in congruent figures

3.1.1.8: [RIT 251 - 255] Identifies congruent triangles using AAS, ASA, SAS, or SSS

3.1.1.9: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent

3.1.1.11: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

3.1.2: Identification and Classification of 2-D Shapes

3.1.2.1: [RIT 230 - 230] Identifies congruent shapes, given formal language

3.1.3: Similarity

3.1.3.1: [RIT 180 - 181] Identifies similar figures

3.1.3.2: [RIT 204 - 253] Applies scale factors to solve problems involving scale drawings, maps, and models

3.1.3.3: [RIT 212 - 212] Determines scale factors in problems involving scale drawings, maps, and models

3.1.3.4: [RIT 212 - 260] Determines lengths of corresponding sides in similar figures

3.1.3.5: [RIT 213 - 226] Identifies corresponding sides and angles in similar figures

3.1.3.6: [RIT 215 - 249] Applies properties of similar triangles to solve real-world problems involving indirect measurements

3.1.3.7: [RIT 220 - 220] Knows the definition of similarity

3.1.3.8: [RIT 223 - 239] Determines scale factors in problems involving scale drawings of geometric figures

3.1.3.10: [RIT 224 - 224] Determines the ratio between perimeters of similar figures

3.1.3.11: [RIT 225 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures

3.1.3.12: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

3.1.3.13: [RIT 232 - 257] Applies properties of similar figures to determine a perimeter

3.1.3.15: [RIT 235 - 235] Applies properties of similar figures to determine an area

3.1.3.16: [RIT 239 - 239] Identifies the proportion of corresponding sides of similar figures

3.1.3.17: [RIT 244 - 263] Applies similarity postulates to solve for missing lengths and angles

3.1.3.18: [RIT 247 - 247] Applies similarity postulates to identify corresponding sides and angles

3.1.3.20: [RIT 256 - 256] Identifies similar triangles using AA

3.1.3.22: [RIT 260 - 279] Applies the geometric mean to solve for missing lengths and angles in triangles

3.1.3.23: [RIT 268 - 271] Identifies the similarity postulate that proves two triangles are similar

3.1.3.26: [RIT 285 - 286] Determines the ratio between areas of similar figures

3.1.3.27: [RIT 288 - 288] Solves problems involving multiple theorems of similar triangles, including the Triangle Proportionality Theorem, segment proportionality property for parallel lines, and similarity postulates

3.1.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

3.1.4.1: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

3.1.4.2: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent

3.1.4.3: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

3.1.4.4: [RIT 268 - 271] Identifies the similarity postulate that proves two triangles are similar

3.2: Pythagorean Theorem, Right Triangle Trig

3.2.1: Pythagorean Theorem

3.2.1.1: [RIT 241 - 275] Uses the Pythagorean Theorem to solve real-world or mathematical problems

3.2.1.2: [RIT 242 - 266] Uses the Pythagorean Theorem to calculate the length of a missing side of a right triangle

3.2.1.3: [RIT 253 - 268] Applies the converse of the Pythagorean Theorem to identify right triangles

3.2.2: Trigonometry

3.2.2.1: [RIT 241 - 263] Represents the sine of an angle as a ratio of sides in a right triangle

3.2.2.2: [RIT 246 - 266] Represents the tangent of an angle as a ratio of sides in a right triangle

3.2.2.3: [RIT 247 - 263] Represents the cosine of an angle as a ratio of sides in a right triangle

3.2.2.4: [RIT 250 - 270] Uses sine, cosine, or tangent to determine the length of a side in a right triangle

3.2.2.6: [RIT 263 - 273] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems

3.2.3: Relationships involving Lines, Angles, and Polygons

3.2.3.1: [RIT 255 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to solve real-world and mathematical problems

3.2.3.2: [RIT 258 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to calculate the length of a missing side of a right triangle

3.3: Transformations and Symmetry

3.3.2: Spatial Concepts and Symmetry

3.3.2.1: [RIT 165 - 228] Determines the number of lines of symmetry in 2-D figures

3.3.2.2: [RIT 206 - 217] Identifies 2-D figures which have rotational symmetry

3.3.2.4: [RIT 275 - 284] Identifies the rotational or reflectional symmetry of a shape

3.3.3: Transformations

3.3.3.1: [RIT 177 - 226] Performs a slide, flip, or turn without using a grid

3.3.3.2: [RIT 197 - 225] Performs a translation, reflection, or rotation, without the coordinate plane

3.3.3.3: [RIT 198 - 227] Describes a single transformation that will map one figure onto another, without the coordinate plane

3.3.3.4: [RIT 199 - 220] Identifies a slide, flip, or turn that will carry a given figure onto another, without a grid

3.3.3.5: [RIT 214 - 214] Identifies the degree of rotation that shows that two given figures are congruent, without a coordinate plane

3.3.3.6: [RIT 214 - 221] Identifies the degree of rotation that will map one figure onto another, without the coordinate plane

3.3.3.8: [RIT 219 - 232] Understands that rigid transformations preserve congruency

3.3.3.9: [RIT 221 - 254] Determines the image of a polygon on a coordinate plane after a reflection or a series of reflections

3.3.3.10: [RIT 223 - 254] Determines the coordinates of the vertices of a polygon after a dilation or a series of dilations, with center at the origin

3.3.3.11: [RIT 225 - 228] Determines the coordinates of the vertices of a polygon after a translation or a series of translations

3.3.3.12: [RIT 226 - 226] Determines the image of a polygon on a coordinate plane after a rotation or a series of rotations

3.3.3.14: [RIT 231 - 259] Determines the coordinates of the vertices of a polygon after a reflection or a series of reflections

3.3.3.15: [RIT 231 - 242] Describes the effects of dilation on lengths and angle measures

3.3.3.16: [RIT 232 - 255] Describes a single transformation that will map one figure onto itself, without the coordinate plane

3.3.3.17: [RIT 233 - 239] Performs a series of translations, reflections, and rotations, without the coordinate plane

3.3.3.18: [RIT 235 - 271] Determines the coordinates of the vertices of a polygon after a rotation or a series of rotations

3.3.3.19: [RIT 237 - 239] Describes a series of transformations that show two shapes are congruent on the coordinate plane

3.3.3.20: [RIT 239 - 239] Represents translations in the plane using matrices

3.3.3.21: [RIT 240 - 240] Determines the image of a translation represented in coordinate notation

3.3.3.24: [RIT 243 - 243] Describes a single transformation that shows two shapes are congruent on the coordinate plane

3.3.3.25: [RIT 249 - 263] Describes a translation using coordinate notation

3.3.3.26: [RIT 250 - 250] Determines the image of a polygon on a coordinate plane after a series of translations, reflections, or rotations

3.3.3.27: [RIT 251 - 251] Determines the image of a dilation represented in coordinate notation

3.3.3.28: [RIT 252 - 252] Identifies the center and scale factor used in a dilation represented in the coordinate plane

3.3.3.29: [RIT 253 - 253] Applies the scale factor in a dilation to solve for unknown lengths

3.3.3.31: [RIT 264 - 264] Determines the image of a reflection represented in coordinate notation

3.4: Coordinate Graphing and Distance

3.4.1: Coordinate Geometry

3.4.1.1: [RIT 181 - 229] Determines the coordinates of points in all four quadrants of a coordinate graph

3.4.1.2: [RIT 187 - 208] Interprets points with whole number coordinates in the first quadrant within the given context

3.4.1.3: [RIT 198 - 221] Determines the coordinates of points in the first quadrant of a coordinate plane

3.4.1.4: [RIT 201 - 218] Counts to find the distance between points on the coordinate plane

3.4.1.6: [RIT 203 - 215] Plots the coordinates of points in the first quadrant of a coordinate plane

3.4.1.7: [RIT 205 - 232] Determines the distance between two points with the same first or second coordinate

3.4.1.8: [RIT 214 - 235] Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices

3.4.1.9: [RIT 215 - 236] Plots points in all four quadrants of a coordinate plane

3.4.1.12: [RIT 242 - 268] Determines the distance between two points on the coordinate plane

3.4.1.15: [RIT 251 - 280] Identifies collinear points