Investigating and Applying Dimension Changes: Area
The student will describe the effects of changing one or more dimensions on the area of a figure.
Applying Triangle Congruence Relationships
Given congruent triangles, the student will justify and apply triangle congruence relationships.
Making Conjectures About Similar Figures
Given problem situations involving similar figures, the student will use and extend similarity properties and transformations to explore and justify conjectures about the given figures.
Developing Algebraic Expressions to Represent Properties of Angles in Circles
Given numerical and/or geometric patterns that represent angle relationships in circles, the student will investigate inscribed angle relationships.
Coordinate Geometry: Midpoint
Given coordinate points the student will use midpoint formulas to solve problems.
Applying Right Triangle Ratios
The student will apply and prove the definition of similar triangles and identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean.
Applying Trigonometric Ratios
Given problem situations involving similar figures, the student will apply and justify triangle similarity relationships such as trigonometric ratios.
Applying Pythagorean Triples
Given problem situations involving similar figures, the student will apply and justify triangle similarity relationships such as Pythagorean triples.
Investigating and Applying Dimension Changes: Perimeter
Given problem situations involving similar figures, the student will describe the effect on perimeter when one or more dimensions of the figure are changed and apply this idea in solving problems.
Investigating and Applying Dimension Changes: Volume
The student will describe the effects of changing one or more dimensions on the volume of a 3-dimensional figure.
Using Logical Reasoning to Prove Conjectures About Quadrilaterals
Given conjectures about quadrilaterals, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.
Making and Verifying Conjectures about Lines
Students will investigate patterns and make conjectures about geometric relationships.
Making and Verifying Conjectures about Polygons
Students will investigate patterns and make conjectures about geometric relationships, including interior angles of polygons.
Making and Verifying Conjectures About Circles
Given information about the relationship(s) witnin one circle or a set of circles, the student will explore special segments and angles of circles.
Writing the Converse, Inverse, and Contrapositive
Given a conditional statement, the student will write its converse, inverse, and contrapositive.
Making and Verifying Conjectures about Three-Dimensional Figures
Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.
Constructing and Justifying Statements about Geometric Figures
Students will distinguish between undefined terms, definitions, postulates, conjectures, and theorems and investigate patterns to make conjectures about geometric relationships.
Using Counter Examples to Disprove Statements That Are False
Given statements about a geometric relationship, the student will use counter examples to disprove statements that are false.
Using Inductive Reasoning to Formulate Conjectures
Students will practice identifying the converse, inverse, and contrapositive of conditional statements.
Using Logical Reasoning to Prove Statements are True
Given statements about a geometric relationship, the student will distinguish between the undefined terms, definitions, postulates, conjectures, and theorems to prove the statements are true.