RLT: Reasoning, Lines, and Transformations

RLT.G.1: The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include

RLT.G.1.a: identifying the converse, inverse, and contrapositive of a conditional statement;

Biconditional Statements
Conditional Statements

RLT.G.1.c: determining the validity of a logical argument.

Chords and Arcs

RLT.G.3: The student will solve problems involving symmetry and transformation. This will include

RLT.G.3.a: investigating and using formulas for determining distance, midpoint, and slope;

Circles
Distance Formula
Slope

RLT.G.3.c: investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and

Holiday Snowflake Designer

RLT.G.3.d: determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

Dilations
Rotations, Reflections, and Translations
Translations

RLT.G.4: The student will construct and justify the constructions of

RLT.G.4.a: a line segment congruent to a given line segment;

Constructing Congruent Segments and Angles

RLT.G.4.b: the perpendicular bisector of a line segment;

Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

RLT.G.4.c: a perpendicular to a given line from a point not on the line;

Constructing Parallel and Perpendicular Lines

RLT.G.4.d: a perpendicular to a given line at a given point on the line;

Constructing Parallel and Perpendicular Lines

RLT.G.4.f: an angle congruent to a given angle;

Constructing Congruent Segments and Angles

RLT.G.4.g: a line parallel to a given line through a point not on the line; and

Constructing Parallel and Perpendicular Lines

RLT.G.4.h: an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Inscribed Angles

T: Triangles

T.G.5: The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include

T.G.5.a: ordering the sides by length, given angle measures;

Triangle Inequalities

T.G.5.b: ordering the angles by degree measure, given side lengths;

Triangle Inequalities

T.G.5.c: determining whether a triangle exists; and

Triangle Inequalities

T.G.5.d: determining the range in which the length of the third side must lie.

Triangle Inequalities

T.G.6: The student, given information in the form of a figure or statement, will prove two triangles are congruent.

Congruence in Right Triangles
Proving Triangles Congruent

T.G.7: The student, given information in the form of a figure or statement, will prove two triangles are similar.

Congruence in Right Triangles
Similar Figures

T.G.8: The student will solve problems, including practical problems, involving right triangles. This will include applying

T.G.8.a: the Pythagorean Theorem and its converse;

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

T.G.8.c: trigonometric ratios.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

PC: Polygons and Circles

PC.G.9: The student will verify and use properties of quadrilaterals to solve problems, including practical problems.

Parallelogram Conditions

PC.G.10: The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the

PC.G.10.a: sum of the interior and/or exterior angles;

Polygon Angle Sum
Triangle Angle Sum

PC.G.10.b: measure of an interior and/or exterior angle; and

Polygon Angle Sum
Triangle Angle Sum

PC.G.10.c: number of sides of a regular polygon.

Polygon Angle Sum

PC.G.11: The student will solve problems, including practical problems, by applying properties of circles. This will include determining

PC.G.11.c: arc length; and

Inscribed Angles

PC.G.12: The student will solve problems involving equations of circles.

Circles

TDF: Three-Dimensional Figures

TDF.G.13: The student will use surface area and volume of three-dimensional objects to solve practical problems.

Surface and Lateral Areas of Prisms and Cylinders

TDF.G.14: The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include

TDF.G.14.a: comparing ratios between lengths, perimeters, areas, and volumes of similar figures;

Perimeters and Areas of Similar Figures
Similar Figures

TDF.G.14.b: determining how changes in one or more dimensions of a figure affect area and/or volume of the figure;

Prisms and Cylinders

TDF.G.14.d: solving problems, including practical problems, about similar geometric figures.

Perimeters and Areas of Similar Figures
Similar Figures