Triangle Classification, Inequalities, and Angle Sums

Identify fundamental geometric elements, analyze line relationships, and classify two-dimensional figures into hierarchical subcategories.

Measure, classify, and construct angles precisely, and solve for unknowns using adjacent, supplementary, complementary, and vertically opposite angle relationships.

Classify triangles across multiple dimensions, construct valid triangles, verify the triangle inequality theorem, and calculate missing interior angles.

Identify circle parts, construct circles using a compass, understand pi as a geometric ratio, and calculate the circumference and area of circles and sectors.

Derive and apply area formulas for parallelograms, triangles, and trapezoids, analyze perimeter-area relationships, and calculate areas of composite and irregular figures.

Understand volume as 3D space measurement, pack prisms with unit cubes without gaps or overlaps, and apply V = l × w × h, V = s³, and V = B × h.

Calculate the volume of composite three-dimensional figures, determine missing dimensions, and measure irregular object volumes using liquid displacement.

Calculate total and lateral surface areas of three-dimensional solids using nets and area summation of polygonal and curved faces.

Identify 3D solids from 2D representations, draw and validate geometric nets, evaluate edge-vertex relationships, and draw multi-view orthogonal projections.