Infinite Geometry - Common Core Alignment Software version 2.05 - Infinite Geometry supports the teaching of Common Core State Standards

Oct 8, 2026

Uploaded by Jiven

Common Core Alignment Software version 2.05 provides an Infinite Geometry curriculum alignment to the Common Core State Standards for High School Geometry. It includes learning targets across transformations in the plane, rigid motions and congruence, geometric theorem proving, and formal constructions using diverse tools. The document further addresses similarity transformations, trigonometric ratios for right triangles, circle theorems and constructions, arc lengths and sector areas, and coordinate-based proofs, including slope criteria for parallel and perpendicular lines.

LanguageEnglish

CategoryExam

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

High School - Geometry (G)

Transformations in the plane

Congruence and rigid motions

Proving geometric theorems

Formal geometric constructions

Similarity transformations

Trigonometric ratios and right triangles

Circle theorems and constructions

Arc lengths and sector areas

Coordinate proofs and slope criteria

Common Core Alignment Software version 2.05 Last revised July 2015 Infinite Geometry supports the teaching of the Common Core State Standards listed below. High School ‐ Geometry (G) Experiment with transformations in the plane 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. G‐CO‐2 G‐CO‐3 G‐CO‐5 G‐CO‐6 G‐CO‐9 G‐CO‐10 G‐CO‐11 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) . | Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself. | | --- | | 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. | | Understand congruence in terms of rigid motions | | 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. | | Prove geometric theorems | | Prove theorems about lines and angles. 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. | | Prove theorems about triangles. Theorems include: measures of interior
angles of a triangle sum to 180°; 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. | | Prove theorems about parallelograms. 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. | Make geometric constructions 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. ) . 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‐13 G‐SRT‐2 G‐SRT‐3 G‐SRT‐4 G‐SRT‐5 G‐SRT‐6 G‐SRT‐8 G‐C‐2 G‐C‐3 G‐C‐4 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | Understand similarity in terms of similarity transformations | | --- | | 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. | | Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar | | Prove theorems involving similarity | | 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. | | Use congruence and similarity criteria for triangles to solve probl

FAQs

What does Infinite Geometry focus on for High School Geometry?

It aligns instruction with High School Geometry standards, emphasizing transformations, congruence, similarity, circle relationships, constructions, and coordinate-based proof methods.

How are transformations described in the document?

Transformations are represented in the plane (e.g., via transparencies or geometry software) and described as functions that map input points to output points, with attention to whether distance and angle are preserved.

What topics related to circles and sectors are included?

The document covers relationships among inscribed angles, radii, and chords, constructions of inscribed and circumscribed circles, tangent line construction from an external point, and formulas for arc lengths and sector areas derived using similarity.

Oct 8, 2026

Uploaded by Jiven