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STANDARDS

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US-NY

Math

New York Math

Geometry: Geometry – Congruence

Experiment with transformations in the plane.

GEO-G.CO.1

Fully covered
Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.

GEO-G.CO.2

Mostly covered
Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.

GEO-G.CO.3

Fully covered
Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that carry the polygon onto itself.

GEO-G.CO.4

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

GEO-G.CO.5

Mostly covered
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.

Understand congruence in terms of rigid motions.

GEO-G.CO.6

Mostly covered
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.

GEO-G.CO.7

Fully covered
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.

GEO-G.CO.8

Fully covered
Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.

Prove geometric theorems.

GEO-G.CO.9

Mostly covered
Prove and apply theorems about lines and angles.

GEO-G.CO.10

Partially covered
Prove and apply theorems about triangles.

GEO-G.CO.11

Mostly covered
Prove and apply theorems about parallelograms.

Make geometric constructions.

GEO-G.CO.12

Not covered
Make, justify, and apply formal geometric constructions.
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GEO-G.CO.13

Mostly covered
Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.