Circles: Circumference, Area, and Circular Rings

Identify, classify, and calculate unknown angle measures using complementary, supplementary, vertical, adjacent, and intersecting line relationships with algebraic equations.

Investigate, classify, and calculate interior and exterior angle sums for triangles, special quadrilaterals, and regular and irregular n-gons.

Construct triangles and geometric figures with compass and straightedge, apply the triangle inequality theorem, and construct angle and segment bisectors.

Derive and apply formulas for perimeter and area of triangles, parallelograms, rhombuses, and trapezoids with consistent metric and customary units.

Calculate the area of complex, composite, and irregular 2D polygons by additive composition and subtractive decomposition.

Identify parts of a circle, derive the constant ratio pi (π = C/d), and calculate circumference, circle area, sector angles, and annulus ring areas.

Plot points in all four quadrants, calculate horizontal and vertical segment lengths using absolute value, and construct polygons to determine coordinate perimeter and area.

Perform, describe, and analyze translations, reflections, and rotations of 2D shapes on coordinate grids using algebraic mapping rules.

Perform and analyze dilations centered at the origin or arbitrary points, calculate scale factors, and explore properties of similar geometric figures.

Analyze line and rotational symmetry in 2D shapes, determine orders of rotation, and investigate regular, semi-regular, and artistic tessellations.

Identify 3D solid structures, interpret and draw 2D orthographic projections (top, front, side), and determine shapes formed by 2D cross-sections.

Construct and interpret scale drawings, architectural floor plans, map routes, three-figure bearings, and cardinal directional bearings.

Unfold 3D solids into 2D nets and calculate total and lateral surface areas of rectangular prisms, triangular prisms, pyramids, and cylinders.

Calculate the volume of cubes and right rectangular prisms with fractional and decimal edges using packing and formulas, and convert between cubic volume and liquid capacity.