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STANDARDS

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US-KY

Math

Kentucky Math

Conceptual Category Geometry: Geometry—Congruence

Cluster: Experiment with transformations in the plane.

HS.G.1

Know and apply precise definitions of the language of Geometry: (MP.3, MP.6)

HS.G.1.a

Not covered
Understand properties of line segments, angles and circle.
(Content unavailable)

HS.G.1.b

Not covered
Understand properties of and differences between perpendicular and parallel lines.
(Content unavailable)

HS.G.2

Representing transformations in the plane. (MP.5, MP.7)

HS.G.2.a

Fully covered
Describe transformations as functions that take points in the plane as inputs and give other points as outputs.

HS.G.2.b

Mostly covered
Compare transformations that preserve distance and angle measures to those that do not.

HS.G.2.c

Fully covered
Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.

HS.G.3(+)

Mostly covered
Develop formal definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. (MP.6, MP.7)

HS.G.4

Understand the effects of transformations of geometric figures. (MP.2, MP.8)

HS.G.4.a

Mostly covered
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.

HS.G.4.b

Not covered
Specify a sequence of transformations that will carry a given figure onto another.
(Content unavailable)

HS.G.4.c

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.

Cluster: Understand congruence in terms of rigid motions.

HS.G.5

Know and apply the concepts of triangle congruence: (MP.3, MP.6)

HS.G.5.a

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.5.b

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

Cluster: Prove geometric theorems.

HS.G.6

Partially covered
Apply theorems for lines, angles, triangles, parallelograms. (MP.2, MP.3)

HS.G.7

Prove theorems about geometric figures. (MP.6, MP.7)

HS.G.7.a

Partially covered
Construct formal proofs to justify theorems for lines, angles and triangles.

HS.G.7.b

Mostly covered
(+) Construct formal proofs to justify theorems for parallelograms.

Cluster: Make geometric constructions.

HS.G.8

Create and apply geometric constructions. (MP.5, MP.6)

HS.G.8.a

Not covered
Make formal geometric constructions with a variety of tools and methods.
(Content unavailable)

HS.G.8.b

Not covered
Apply basic construction procedures to construct more complex figures.
(Content unavailable)