### G.CO: Congruence

#### 1.1: Experiment with transformations in the plane.

G.CO.1: Verify experimentally (for example, using patty paper or geometry software) the properties of rotations, reflections, translations, and symmetry:

G.CO.1a: Lines are taken to lines, and line segments to line segments of the same length.

G.CO.1b: Angles are taken to angles of the same measure.

G.CO.1c: Parallel lines are taken to parallel lines.

G.CO.2: Recognize transformations as functions that take points in the plane as inputs and give other points as outputs and describe the effect of translations, rotations, and reflections on two-dimensional figures.

#### 1.2: Understand congruence in terms of rigid motions.

G.CO.3: Given two congruent figures, describe a sequence of rigid motions that exhibits the congruence (isometry) between them using coordinates and the non-coordinate plane.

G.CO.5: Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G.CO.6: Demonstrate triangle congruence using rigid motion (ASA, SAS, and SSS).

#### 1.3: Construct arguments about geometric theorems using rigid transformations and/or logic.

G.CO.7: Construct arguments about lines and angles using theorems. 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. (Building upon standard in 8th grade Geometry.)

#### 1.4: Make geometric constructions.

G.CO.11: 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.12: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

### G.SRT: Similarity, Right Triangles, and Trigonometry

#### 2.1: Understand similarity in terms of similarity transformations.

G.SRT.1: Use geometric constructions to verify the properties of dilations given by a center and a scale factor:

G.SRT.1a: 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.1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G.SRT.2: Recognize transformations as functions that take points in the plane as inputs and give other points as outputs and describe the effect of dilations on two-dimensional figures.

G.SRT.4: Understand the meaning of similarity for two-dimensional figures as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

#### 2.2: Construct arguments about theorems involving similarity.

G.SRT.5: Construct arguments about triangles using theorems. 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, and AA.

G.SRT.6: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

#### 2.3: Define trigonometric ratios and solve problems involving right triangles.

G.SRT.7: Show that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G.SRT.9: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

### G.C: Circles

#### 3.1: Understand and apply theorems about circles.

G.C.2: 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.4: Construct inscribed and circumscribed circles for triangles.

G.C.5: Construct inscribed and circumscribed circles for polygons and tangent lines from a point outside a given circle to the circle.

### G.GPE: Expressing Geometric Properties with Equations

#### 4.1: Translate between the geometric description and the equation for a conic section.

G.GPE.1: Write the equation of a circle given the center and radius or a graph of the circle; use the center and radius to graph the circle in the coordinate plane.

G.GPE.2: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; graph the circle in the coordinate plane;

G.GPE.3: Complete the square to find the center and radius of a circle given by an equation.

G.GPE.4: Derive the equation of a parabola given a focus and directrix; graph the parabola in the coordinate plane.

G.GPE.5: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; graph the ellipse or hyperbola in the coordinate plane.

### G.GMD: Geometric Measurement and Dimension

#### 5.1: Explain volume formulas and use them to solve problems.

G.GMD.1: 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 and informal limit arguments.

G.GMD.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a solid figure.

Correlation last revised: 9/24/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.