Texas Gateway: Making and Verifying Conjectures About Circles

Given the relationship(s) among a set of angles, the student investigates the patterns and makes conjectures about the geometric relationships, including angles formed by parallel lines cut by a transversal.

Students will investigate patterns and make conjectures about geometric relationships.

Students will investigate patterns and make conjectures about geometric relationships, including interior angles of polygons.

Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.

Given examples of triangles and their component parts, the student will use explorations and concrete models to verify and apply the and find the sum of interior angles.

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.

Given information about the properties of polygons, students will verify theorems about the relationships, including the sum of interior angles, and apply these relationships to solve problems.

The student will verify theorems about angles formed by parallel lines cut by a transversal and apply these relationships to solve problems.

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.