Growth: Grades 6+ Math - Geometry (2017) Gizmos | Browse by Core Curriculum

3: Geometry

3.1: 2-D and 3-D Identification and Classification

3.1.1: Identification and Classification of 2-D Shapes

3.1.1.1: [RIT 148 - 180] Identifies and names triangles, squares, rectangles, and circles

3.1.1.3: [RIT 156 - 190] Identifies the number of sides or corners of 2-D shapes, given pictures

3.1.1.4: [RIT 160 - 181] Knows definitions of a triangle, a square, a rectangle, and a circle

3.1.1.6: [RIT 171 - 180] Sorts shapes based on shared attributes

3.1.1.7: [RIT 176 - 219] Identifies a polygon

3.1.1.9: [RIT 197 - 222] Identifies and names nonbasic shapes, such as trapezoids, hexagons, etc.

3.1.1.10: [RIT 201 - 235] Identifies and names special triangles, such as acute, right, scalene, etc., given pictures

3.1.1.11: [RIT 201 - 224] Identifies properties of a 2-D shape, such as right angles, parallel sides, etc., given pictures

3.1.1.12: [RIT 203 - 221] Understands the relationships among categories of shapes

3.1.1.13: [RIT 204 - 236] Knows definitions of special triangles, such as acute, right, scalene, etc.

3.1.1.14: [RIT 206 - 224] Classifies 2-D shapes by properties, given pictures

3.1.1.15: [RIT 207 - 207] Knows definitions of nonbasic shapes, such as trapezoids, hexagons, etc.

3.1.1.16: [RIT 212 - 214] Identifies properties of a 2-D shape, such as right angles, parallel sides, etc., without pictures given

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

3.1.1.18: [RIT 213 - 260] Knows properties of parallelograms, including special parallelograms such as squares, rhombuses, etc.

3.1.2: Identification and Classification of 3-D Shapes

3.1.2.1: [RIT 154 - 195] Identifies and names cubes, cones, cylinders, and spheres

3.1.2.3: [RIT 179 - 186] Identifies and names rectangular prisms

3.1.2.4: [RIT 179 - 199] Identifies the number of faces, edges, or vertices for a 3-D object, given pictures

3.1.2.5: [RIT 191 - 228] Identifies faces, bases, edges, or vertices of 3-D shapes

3.1.2.6: [RIT 191 - 191] Describes polyhedrons based on the shapes of faces, and/or number of faces, edges, or vertices, given pictures

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

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

3.1.2.11: [RIT 254 - 254] Compares 3-D figures based on the shapes of faces and/or number of faces, edges, or vertices

3.2: Spatial Reasoning, Similarity, Congruence & Scale Factors

3.2.1: Congruence

3.2.1.1: [RIT 153 - 184] Identifies congruent shapes, given informal language

3.2.1.2: [RIT 189 - 218] Identifies congruent shapes, given formal language

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

3.2.1.7: [RIT 229 - 229] Uses formal notation to denote corresponding sides and angles in congruent triangles

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

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

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

3.2.1.12: [RIT 252 - 277] Identifies the congruence postulate that proves two triangles are congruent

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

3.2.2: Similarity

3.2.2.1: [RIT 180 - 181] Identifies similar figures

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

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

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

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

3.2.2.6: [RIT 213 - 213] Knows the definition of similarity

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

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

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

3.2.2.11: [RIT 224 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures

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

3.2.2.14: [RIT 237 - 257] Applies properties of similar figures to determine a perimeter

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

3.2.2.16: [RIT 243 - 263] Applies similarity postulates to solve for missing lengths and angles

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

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

3.2.2.21: [RIT 260 - 276] Applies the geometric mean to solve for missing lengths and angles in triangles

3.2.2.22: [RIT 263 - 276] Determines the conditions necessary to prove two triangles are similar

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

3.2.2.25: [RIT 283 - 283] Solves problems involving multiple theorems of similar triangles, including the Triangle Proportionality Theorem, segment proportionality property for parallel lines, and similarity postulates

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

3.2.3: Spatial Concepts and Symmetry

3.2.3.2: [RIT 162 - 180] Recognizes lines of symmetry in 2-D figures

3.2.3.3: [RIT 170 - 217] Identifies the figure formed by folding and/or cutting a shape

3.2.3.4: [RIT 171 - 202] Composes or decomposes 2-D shapes to form new shapes

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

3.2.3.6: [RIT 177 - 177] Identifies 3-D shapes given multiple views

3.2.3.7: [RIT 180 - 202] Identifies 2-D figures which have line symmetry

3.2.3.8: [RIT 181 - 220] Determines the number of lines of symmetry in 2-D figures

3.2.3.9: [RIT 185 - 234] Identifies and creates nets for prisms

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

3.2.3.11: [RIT 195 - 222] Identifies and creates nets for cones

3.2.3.12: [RIT 206 - 206] Composes or decomposes 3-D shapes to form new shapes

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

3.2.3.14: [RIT 211 - 225] Identifies single views of 3-D shapes

3.2.3.15: [RIT 213 - 249] Identifies single views of structures composed of cubes

3.2.3.16: [RIT 219 - 236] Identifies and creates nets for cylinders

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

3.2.3.21: [RIT 260 - 260] Identifies the rotational or reflectional symmetry of a shape

3.2.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

3.2.4.1: [RIT 252 - 277] Identifies the congruence postulate that proves two triangles are congruent

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

3.2.4.3: [RIT 263 - 276] Determines the conditions necessary to prove two triangles are similar

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

3.3: Lines, Angles, Polygons, and Coordinate Geometry

3.3.1: Coordinate Geometry

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

3.3.1.3: [RIT 205 - 237] Determines the distance between two points with the same first or second coordinate

3.3.1.4: [RIT 209 - 236] Determines the coordinates of points in all four quadrants of a coordinate graph

3.3.1.5: [RIT 214 - 236] Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices

3.3.1.9: [RIT 235 - 235] Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate

3.3.1.10: [RIT 242 - 266] Determines the distance between two points on the coordinate plane

3.3.1.13: [RIT 251 - 273] Identifies collinear points

3.3.1.24: [RIT 264 - 264] Determines the perimeter of a triangle given the coordinates of the vertices

3.3.2: Circles

3.3.2.1: [RIT 237 - 279] Writes the equation of a circle given the center and radius

3.3.2.2: [RIT 257 - 275] Writes the equation of a circle given a graph

3.3.2.3: [RIT 267 - 273] Graphs a circle given the equation

3.3.2.4: [RIT 272 - 272] Determines the center and radius given the standard form of the equation

3.3.2.5: [RIT 275 - 275] Writes the equation of a circle given the center and a point on the circle

3.3.2.6: [RIT 278 - 286] Determines the center and radius of a circle given the general form of the equation

3.3.3: Conic Sections

3.3.3.1: [RIT 237 - 279] Writes the equation of a circle given the center and radius

3.3.3.2: [RIT 247 - 271] Identifies the conic section from the equation

3.3.3.3: [RIT 257 - 275] Writes the equation of a circle given a graph

3.3.3.4: [RIT 267 - 273] Graphs a circle given the equation

3.3.3.5: [RIT 268 - 268] Writes the equation of an ellipse given the center and vertices

3.3.3.6: [RIT 268 - 268] Graphs a parabola with an axis of symmetry parallel to the x-axis

3.3.3.7: [RIT 272 - 272] Determines the center and radius given the standard form of the equation

3.3.3.8: [RIT 275 - 275] Writes the equation of a circle given the center and a point on the circle

3.3.3.9: [RIT 278 - 286] Determines the center and radius of a circle given the general form of the equation

3.3.4: Geometric Constructions

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

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

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

3.3.5.1: [RIT 181 - 203] Identifies parallel lines involving real-world objects

3.3.5.2: [RIT 185 - 198] Identifies intersecting lines

3.3.5.3: [RIT 186 - 213] Identifies right angles

3.3.5.4: [RIT 193 - 210] Identifies parallel lines

3.3.5.5: [RIT 201 - 229] Identifies acute or obtuse angles

3.3.5.6: [RIT 202 - 229] Identifies points, lines, rays, line segments, and angles

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

3.3.5.8: [RIT 205 - 205] Recognizes precise definitions of parallel and perpendicular lines

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

3.3.5.10: [RIT 222 - 228] Understands what the measure of an angle represents

3.3.5.11: [RIT 227 - 243] Identifies perpendicular lines

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

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

3.3.6: Angle Measurement

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

3.3.6.2: [RIT 222 - 228] Understands what the measure of an angle represents

3.3.6.3: [RIT 226 - 235] Knows the definition of an angle

3.3.7: Relationships involving Lines, Angles, and Polygons

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

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

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

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

3.3.7.5: [RIT 226 - 246] Applies the Triangle Angle-Sum Theorem to determine the measure of an unknown angle

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

3.3.7.7: [RIT 230 - 255] Solves problems involving parallel lines cut by a transversal

3.3.7.8: [RIT 230 - 230] Determines the number of diagonals that can be drawn from one vertex in a polygon

3.3.7.10: [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

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

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

3.3.7.14: [RIT 242 - 243] Applies the Triangle Exterior Angle Theorem to determine the measure of an unknown angle

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

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

3.3.7.17: [RIT 253 - 260] Determines the conditions necessary to show that two lines are parallel

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

3.3.7.19: [RIT 258 - 258] Applies the formula for the measure of each interior angle of a regular polygon

3.3.7.21: [RIT 280 - 280] Identifies vertical angles

3.3.8: Geometric Proof/Logic/Inductive and Deductive Reasoning

3.3.8.1: [RIT 253 - 260] Determines the conditions necessary to show that two lines are parallel

3.3.8.2: [RIT 275 - 275] Proves theorems involving the properties of parallelograms

3.4: Transformations

3.4.1: Transformations

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

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

3.4.1.3: [RIT 202 - 225] Performs a translation, reflection, or rotation, without the coordinate plane

3.4.1.4: [RIT 208 - 208] Knows the definition of a slide, a flip, or a turn

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

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

3.4.1.7: [RIT 218 - 232] Describes a single transformation that will map one figure onto another, without the coordinate plane

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

3.4.1.9: [RIT 223 - 260] Determines the coordinates of the vertices of a polygon after a dilation or a series of dilations, with center at the origin

3.4.1.11: [RIT 224 - 232] Understands that rigid transformations preserve congruency

3.4.1.12: [RIT 226 - 230] Determines the coordinates of the vertices of a polygon after a translation or a series of translations

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

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

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

3.4.1.17: [RIT 232 - 272] Describes a single transformation that will map one figure onto itself, without the coordinate plane

3.4.1.18: [RIT 236 - 244] Determines the coordinates of the vertices of a polygon after a rotation or a series of rotations

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

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

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

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

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

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

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

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

3.4.1.29: [RIT 285 - 285] Describes the effects of dilation on areas

3.5: Pythagorean Theorem, Trigonometry & Special Right Triangles

3.5.1: Pythagorean Theorem

3.5.1.1: [RIT 240 - 266] Uses the Pythagorean Theorem to calculate the length of a missing side of a right triangle

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

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

3.5.2: Trigonometry

3.5.2.2: [RIT 240 - 267] Represents the tangent of an angle as a ratio of sides in a right triangle

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

3.5.2.4: [RIT 247 - 267] Represents the cosine of an angle as a ratio of sides in a right triangle

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

3.5.2.7: [RIT 263 - 266] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems

3.5.3: Relationships involving Lines, Angles, and Polygons

3.5.3.1: [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

3.5.3.2: [RIT 259 - 275] Uses the 45-45-90 and 30-60-90 right triangle relationships to solve real-world and mathematical problems

3.6: Circles

3.6.1: Circles

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

3.6.1.2: [RIT 238 - 263] Understands that the ratio between the circumference and the diameter of a circle is equal to pi

3.6.1.3: [RIT 242 - 286] Uses properties of central and inscribed angles to solve problems involving circles

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

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

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

3.6.1.9: [RIT 263 - 274] Calculates arc lengths

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