high school geometry

high school geometry

Here you will find all high school geometry resources to guide and support mathematics teaching and learning.

These resources are organized by mathematical strand and refer to specific Common Core math content standards.

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G-CO.1

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.

Problems of the Month

G-CO.2

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).

Problems of the Month

G-CO.3

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Problems of the Month

G-CO.4

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.5

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.

Problems of the Month

G-CO.7

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.

Problems of the Month

G-CO.8

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Problems of the Month

G-CO.9

Prove theorems about lines and angles.

Problems of the Month

Performance Assessment Tasks

G-CO.10

Prove theorems about triangles.

Problems of the Month

Performance Assessment Tasks

G-CO.11

Prove theorems about parallelograms.

Problems of the Month

Performance Assessment Tasks

G-CO.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

G-CO.13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Problems of the Month

G-SRT.1

Verify experimentally the properties of dilations given by a center and a scale factor.

Problems of the Month

G-SRT.2

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.

Performance Assessment Tasks

G-SRT.5

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

Performance Assessment Tasks

G-SRT.6

Understand 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.

Performance Assessment Tasks

G-SRT.7

Explain and use the relationship between the sine and cosine of complementary angles.

Performance Assessment Tasks

G-SRT.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Performance Assessment Tasks

G-SRT.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Problems of the Month

G-C.2

Identify and describe relationships among angles, radii, and chords. Include the relationship between central, inscribed and circumscribes 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.

Problems of the Month

Performance Assessment Tasks

G-C.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Problems of the Month

Performance Assessment Tasks

G-GMD.4

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Problems of the Month

G-MG.1

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Problems of the Month

G-MG.2

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

Problems of the Month

G-MG.3

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).