Circles Benchmark Students investigate properties of circles focusing on relationships among angles, arcs, lines, and chords. Indicators Use appropriate vocabulary to identify and describe circles and their related parts. Apply relationships among tangents, radii, and chords to solve problems involving measurement in circles. Determine circumference, arc length, and areas of circles, sectors, and segments. Solids Benchmark Students investigate polyhedrons by extending concepts of plane geometry to three space.
Indicators Sketch polyhedrons and identify relevant parts.
Investigate right triangles in cones, pyramids, and spheres. Informally derive and use formulas for determining surface area and volume of a variety of nonoblique solids and apply these in real-world situations. Investigate ratios of areas and volumes of similar solids. Logic and Proof Benchmark Students apply several alternative methods for producing deductive arguments to verify hypotheses. Indicators Use inductive and deductive reasoning, including the law of syllogism, as a means for developing logical arguments.