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Основно съдържание

STANDARDS

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US-ND

Math

North Dakota Math

High School—Geometry: Congruence

Experiment with transformations in the plane

HS.G-CO.1

Fully covered
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane.

HS.G-CO.2

Mostly covered
Represent transformations in the plane. 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).

HS.G-CO.3

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

HS.G-CO.4

Mostly covered
Develop or verify experimentally the characteristics of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

HS.G-CO.5

Mostly covered
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

HS.G-CO.6

Mostly covered
Use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure. Use the definition of congruence in terms of rigid motions to decide if two figures are congruent.

HS.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.

HS.G-CO.8

Fully covered
Prove two triangles are congruent using the congruence theorems such as ASA, SAS, and SSS.

Prove and apply geometric theorems

HS.G-CO.9

Mostly covered
Prove and apply theorems about lines and angles.

HS.G-CO.10

Partially covered
Prove and apply theorems about triangle properties.

HS.G-CO.11

Fully covered
Prove and apply theorems about parallelograms.

Make geometric constructions

HS.G-CO.12

Not covered
Make basic geometric constructions with a variety of tools and methods.
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HS.G-CO.13

Partially covered
(+)Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.