Texas Gateway: Making Conjectures About Circles and Angles

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.

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 and relationships among the resulting segments.

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 examples of quadrilaterals and their component parts, the student will use explorations and concrete models to prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or...

Given geometric figures on the coordinate plane, the student will apply the definition of congruence, in terms of rigid transformations, to identify congruent figures. The student will also identify and distinguish between reflectional...

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

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, including interior angles of polygons.

Students will investigate patterns and make conjectures about geometric relationships.