Geometry illustration

Geometry

ISEE Upper Level

Properties of shapes, angles, coordinate geometry, transformations, and area/perimeter/volume computation — excludes unit conversions (see measurement)

10 topics

Segments & Lengths

Segment arithmetic, midpoints, bisectors, and line segment relationships — 1D geometry without angle measurement

Angles

Angle relationships (supplementary, complementary, vertical), parallel line angles, and interior angle sums of polygons

Triangles

Triangle area, Pythagorean theorem, angle sums, congruence, and similarity — excludes general area/perimeter of other shapes (see area-perimeter-composite)

Circles

Circumference, area, arcs, sectors, central angles, and radius/diameter — excludes composite shapes involving circles (see area-perimeter-composite)

Polygons

Properties of quadrilaterals, regular polygons, and symmetry

Coordinate Geometry

Plotting points, distance, midpoint, and slope on the coordinate plane — excludes graphing linear equations (see linear-graphing)

Transformations

Reflections, rotations, translations, and symmetry

Area, Perimeter & Composite Shapes

Calculating perimeter and area of rectangles, squares, parallelograms, trapezoids, and composite/irregular shapes — excludes circles (see circles) and triangles (see triangles)

Volume & Surface Area

Calculating volume and surface area of prisms, cylinders, cones, and spheres

Visual & Spatial Reasoning

Non-coordinate spatial reasoning: net folding, cube counting/painting, paper folding, figure rotation recognition, and 3D visualization — excludes coordinate-based transformations (see transformations)

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