Geometry

Select a Standard:

CCircles
CCircles
Geometry Logo. Includes four pictures of solids on an orange background.
Prove that all circles are similar.
G-C.1.1
Geometry Logo. Includes four pictures of solids on an orange background.
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
G-C.2.5
Geometry Logo. Includes four pictures of solids on an orange background.
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-C.1.2
Geometry Logo. Includes four pictures of solids on an orange background.
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G-C.1.3
COCongruence
COCongruence
Geometry Logo. Includes four pictures of solids on an orange background.
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.1.1
Geometry Logo. Includes four pictures of solids on an orange background.
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G-CO.1.4
Geometry Logo. Includes four pictures of solids on an orange background.
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.2.7
Geometry Logo. Includes four pictures of solids on an orange background.
Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; 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.3.10
Geometry Logo. Includes four pictures of solids on an orange background.
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
G-CO.4.13
Geometry Logo. Includes four pictures of solids on an orange background.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G-CO.1.2
Geometry Logo. Includes four pictures of solids on an orange background.
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
G-CO.1.5
Geometry Logo. Includes four pictures of solids on an orange background.
Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.
G-CO.2.8
Geometry Logo. Includes four pictures of solids on an orange background.
Prove theorems about parallelograms; use theorems about parallelograms to solve problems. 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.3.11
Geometry Logo. Includes four pictures of solids on an orange background.
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G-CO.1.3
Geometry Logo. Includes four pictures of solids on an orange background.
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.2.6
Geometry Logo. Includes four pictures of solids on an orange background.
Prove theorems about lines and angles; use theorems about lines and angles to solve problems. 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.3.9
Geometry Logo. Includes four pictures of solids on an orange background.
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-CO.4.12
GMDGeometric Measurement and Dimension
GMDGeometric Measurement and Dimension
Geometry Logo. Includes four pictures of solids on an orange background.
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
G-GMD.1.1
Geometry Logo. Includes four pictures of solids on an orange background.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★
G-GMD.1.3
Geometry Logo. Includes four pictures of solids on an orange background.
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
G-GMD.2.4
GPEExpressing Geometric Properties With Equations
GPEExpressing Geometric Properties With Equations
Geometry Logo. Includes four pictures of solids on an orange background.
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
G-GPE.1.1
Geometry Logo. Includes four pictures of solids on an orange background.
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G-GPE.2.6
Geometry Logo. Includes four pictures of solids on an orange background.
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.2.4
Geometry Logo. Includes four pictures of solids on an orange background.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. ★
G-GPE.2.7
Geometry Logo. Includes four pictures of solids on an orange background.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G-GPE.2.5
MGModeling With Geometry
MGModeling With Geometry
Geometry Logo. Includes four pictures of solids on an orange background.
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★
G-MG.1.1
Geometry Logo. Includes four pictures of solids on an orange background.
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). ★
G-MG.1.2
Geometry Logo. Includes four pictures of solids on an orange background.
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★
G-MG.1.3
SRTSimilarity, Right Triangles, and Trigonometry
SRTSimilarity, Right Triangles, and Trigonometry
Geometry Logo. Includes four pictures of solids on an orange background.
Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G-SRT.1.1.a
Geometry Logo. Includes four pictures of solids on an orange background.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G-SRT.1.3
Geometry Logo. Includes four pictures of solids on an orange background.
Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.3.7
Geometry Logo. Includes four pictures of solids on an orange background.
Verify experimentally the properties of dilations given by a center and a scale factor: b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G-SRT.1.1.b
Geometry Logo. Includes four pictures of solids on an orange background.
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.2.4
Geometry Logo. Includes four pictures of solids on an orange background.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
G-SRT.3.8
Geometry Logo. Includes four pictures of solids on an orange background.
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.1.2
Geometry Logo. Includes four pictures of solids on an orange background.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G-SRT.2.5
Additional Course Resources
Additional Course Resources
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Geometry EOC Practice
Geometry EOC Practice
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Click on this text to download the Answer KEY for the PARCC Summative for Geometry.
PARCC Spring 2016 Answer KEY Paper Based Practice
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Three additional Geometry EOC practice tests with answer keys.
More Geometry EOC Practice
Document symbol in gray on a green background.
Click on this text to download the PARCC Summative Practice Test for Geometry.
PARCC Spring 2016 Paper Based Practice