# Concepts and Principles of Geometry

## Skills and Concepts

RIT scores between 151 and 160
Shapes and Figures, 2- and 3-dimensional
· Identify and name the plane figures: circle, triangle, and square
Congruency and Similarity
· Identify congruent figures (using “same size and shape” terminology)
· Identify figures that are similar, have the same shape

RIT scores between 161 and 170
Shapes and Figures, 2- and 3-dimensional
· Identify and name solid figures: can (cylinder) and cone
· Relate and compare plane figures to solid figures
· Identify sides and corners (vertices) on solid figures
· Contrast open and closed figures
· Identify cylinder (can) attributes
Congruency and Similarity
Identify congruent figures

RIT scores between 171 and 180
Shapes and Figures, 2- and 3-dimensional
· Classify and sort solid figures
Congruency and Similarity
· Identify congruent figures using terminology
Symmetry and Transformations
· Recognize transformations of plane figures (slides, flips, and turns) by identifying the figure that
will fit in a certain space
Direction and Distance
· Identify position concepts: over, under, inside, outside, in front, behind, top, middle, bottom
Coordinate
· Graph ordered pairs in the first quadrant

RIT scores between 181 and 190
Shapes and Figures, 2- and 3-dimensional
· Identify and name the plane figures: circle, triangle, square, and rectangle
· Recognize solid figures: cube (box)
· Identify characteristics of plane figures (sides and corners)
Congruency and Similarity
· Identify congruent figures, angles, and line segments
· Identify similar figures (same shape, may or may not be same size)
Symmetry and Transformations
· Identify figures with line symmetry
· Recognize transformations of plane figures (slides, flips, and turns)
· Identify types of transformations (slides, flips, and turns)
Line Properties and Terminology
· Identify points on a line
· Identify the correct label for a line
Coordinate
· Graph ordered pairs in the first quadrant

RIT scores between 191 and 200
Shapes and Figures, 2- and 3-dimensional
· Recognize solid figures: sphere (ball)
· Identify and name solid figures: cube, cylinder, cone, rectangular prism, and sphere
· Identify characteristics of plane figures (sides and corners)
Symmetry and Transformations
· Identify figures with line symmetry and symmetrical parts
Geometric Properties and Terminology
· Identify position concepts: (over, under, inside, outside, in front, behind, top, middle, bottom)
· Describe and measure right angles
· Identify right angles
· Identify intersecting, parallel lines
· Identify the diagonal of a circle

RIT scores between 201 and 210
Shapes and Figures, 2- and 3-dimensional
· Identify faces, edges, and corners (vertices) on solid figures
· Identify polygons: triangle, quadrilateral, pentagon, and octagon
· Identify quadrilaterals: square, rectangle, and parallelogram
· Identify, name, and analyze solid figures: cube, cylinder, triangular pyramid and square pyramid
(faces, edges, and vertices)
Symmetry and Transformations
· Identify mirror-images
Congruency and Similarity
· Identify congruent figures, angles and line segments
Geometric Properties and Terminology
· Identify points, lines, line segments, rays, planes, and angles
· Identify the diameter of a circle
· Identify intersecting, parallel, and perpendicular lines
· Calculate the surface area of a rectangular prism
· Identify angles according to their measure: right, obtuse, and acute

RIT scores between 211 and 220
Shapes and Figures, 2- and 3-dimensional
· Identify faces, edges, and corners (vertices) on solid figures
· Contrast open and closed figures
· Identify polygons: triangle, quadrilateral, pentagon, hexagon, and octagon
· Identify quadrilaterals: square, rectangle, parallelogram, trapezoid, rhombus
· Analyze solid figures: triangular pyramid and rectangular pyramid (faces, edges, and vertices)
Congruency and Similarity
· Identify similar figures (same shape, may or may not be the same size)
· Identify congruent polygons and their corresponding sides and angles
Symmetry and Transformations
· Identify types of transformations (rotation)
Geometric Properties and Terminology
· Identify points, lines, line segments, rays, and angles
· Identify angles: right, obtuse, and acute
· Identify when two intersecting lines are perpendicular
· Identify properties of similar figures
· Measure angles using a protractor

RIT scores between 221 and 230
Shapes and Figures, 2- and 3-dimensional
· Analyze solid figures: rectangular prism, triangular prism, triangular pyramid, square, pyramid
(faces, edges and vertices)
· Classify polygons by sides and angles
Congruency and Similarity
· Identify congruent triangles according to corresponding parts (SSS, SAS, ASA)
Geometric Properties and Terminology
· Identify the center, radius and diameter of a circle
· Measure angles using a protractor
· Classify angles: supplementary and complementary
· Classify angles: adjacent, vertical, corresponding, and supplementary
· Find the missing angle measurement in a triangle when two angles are known
· Analyze circles: center, chord, diameter, radius, arc, semicircle, and circumference
Coordinate
· Graph ordered pairs in all four quadrants ( coordinate geometry )

RIT scores between 231 and 240
Symmetry and Transformations
· Understand meaning and representation of a dilation
Geometric Properties and Terminology
· Classify triangles by sides (equilateral, isosceles, and scalene) and angles (acute, obtuse, and
right)
· Classify polygons by sides and angles
· Identify and discriminate between regular and irregular polygons
· Find the missing angle measurement in a triangle when two angles are known
· Solve word problems involving similar polygons
· Identify the base angles of a triangle
· Know the definition of the hypotenuse of a triangle
· Calculate the circumference of a circle using the formula
Coordinate
· Find location of coordinates on a number line
· Locate the vertex on a coordinate grid

RIT scores between 241 and 250
Congruency and Similarity
· Construct congruent segments and angles
Symmetry and Transformations
· Identify symmetry of a sphere
Geometric Properties and Terminology
· Identify properties of parallel lines
· Construct angle bisectors
· Use the Pythagorean theorem to calculate the measure of one side of a right triangle when the
other two sides are known
· Identify angle bisectors
· Solve problems regarding relationships among chords of a circle
· Calculate the surface area of a rectangular prism and cylinder
Coordinate
· Determine endpoints and midpoint of a line on a coordinate graph

RIT scores between 251 and 260
Congruency and Similarity
· Solve problems involving properties of similar triangles
Symmetry and Transformations
· Solve problems involving rotations (turns) and reflections (flips)
Geometric Properties and Terminology
· Identify properties and slope of lines
· Identify plane
· Identify midpoint and endpoint
· Identify perpendicular bisector
· Identify properties of polygons (rhombus, parallelogram)
· Relationship of size of angles and corresponding sides of a triangle
Trigonometry
· Find sin and cosine of a given angle
Coordinate
· Derive and solve problems involving use of ordered pairs to determine area of a figure
· Know the effect of rigid motions on figures in the coordinate plane and space, including
rotations, translations, and reflections
· Determine the axis of symmetry of a linear graph

RIT scores between 261 and 270
Geometric Properties and Terminology
· Identify the correct definition of a postulate
· Solve problems using two chord power theorem
· Identify and solve problems involving right triangles using the trigonometric functions and the
Pythagorean Theorem
· Use of distance formula to determine type of triangle using coordinates
· Solve problems regarding relationships among chords, secants, tangents, inscribed angles,
central angle, arc, and inscribed and circumscribed polygons of circles
· Measure and compare angles in degrees
· Solve problems involving the perimeter, circumference, area, volume, and surface area of
common geometric figures
· Determine how changes in dimensions affect the perimeter, area, and volume of common
geometric figures and solids
· Find and use measures of sides and interior and exterior angles to identify figures and solve
problems involving polygons
· Know the effect of rigid motions on figures in the coordinate plane and space, including
rotations, translations, and reflections
· Find the surface area of a polyhedron and cylinder
· Find the diameters when given the area of a circle
Trigonometry
· Use graph to identify trigonometric functions of angles
· Find cosine, sine, and tangent of any given angle
· Use law of cosines

RIT scores between 271 and 280
Congruency and Similarity
· Prove that triangles and other polygons are congruent or similar using algebraic , coordinate, and
deductive proofs
Geometric Properties and Terminology
· Identify number of diagonals of regular polygons
· Informally prove relationships between angles in polygons by using properties of
complementary, supplementary, vertical, and exterior angles

RIT scores between 281 and 290
Symmetry and Transformations
· Solve problems involving volume with rotational transformation

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