Geometry & Figures

45 problem types

Angle Facts in a Figure

A clock face is twelve equal 30-degree parts Measurement & data

A straight line is 180 degrees Measurement & data

Adjacent angles of a parallelogram sum to 180 Geometry

Corresponding and alternate angles are equal Geometry

Draw an auxiliary parallel line to find a bent angle Geometry

Exterior angle sum of a regular polygon is 360 GeometryMeasurement & data

Perpendicular is half of a straight angle GeometryMeasurement & data

Polygon angle sum via triangulation from a vertex Geometry

Quadrilateral angles sum to 360 degrees Measurement & data

Small angles combine into larger angles Measurement & data

Split a polygon into triangles to sum angles Measurement & data

Triangle angles sum to 180 degrees Measurement & data

Use the 180-degree line to find figure angles Measurement & data

Isosceles and Equilateral Angle Chaining

Chain isosceles base angles to find unknown angles Measurement & dataGeometry

Equal point distances make isosceles triangles on a peg board Geometry

Isosceles triangle from a rectangle diagonal GeometryMeasurement & data

Spot equal sides to build isosceles triangles Measurement & dataGeometry

Two radii form an isosceles triangle; find angles Measurement & dataGeometry

Use equilateral 60-degree angles and equal sides GeometryMeasurement & data

Transformations Preserve Measures

Center of rotation stays fixed Measurement & data

Even number of flips returns original Geometry

Flip across a line creates symmetry Geometry

Flipping or turning digits forms new digits Geometry

Folded angles are equal; chain to the unknown Measurement & data

Folding makes congruent corresponding angles Geometry

Four 90-degree turns return original Measurement & data

Rotation preserves side lengths and angle measures Measurement & data

Quadrilateral Diagonal Properties

Diagonals of a parallelogram bisect each other Geometry

Square diagonals are equal and perpendicular bisectors GeometryMeasurement & data

Radius and Diameter Relationships

All radii in one circle are equal Measurement & dataGeometry

Center to edge distance is the radius Measurement & dataGeometry

Diameter is twice the radius OperationsGeometry

Find each radius and diameter from segments OperationsGeometry

Perimeter of shape joining circle centers Measurement & dataOperations

Perimeter of shapes from tangent circles Measurement & dataOperations

Perimeter splits into radius arcs and straight parts Measurement & dataGeometry

Polygon side equals sum of two radii Measurement & dataGeometry

Rectangle sides are multiples of the diameter OperationsGeometry

Segment through chained centers as radius multiples OperationsGeometry

Triangle side equals sum of two radii Measurement & dataGeometry

Systematically Count Shapes in a Figure

Count all shapes hidden in a grid GeometryOperations

Count all the rhombuses in a figure of small triangles Geometry

Count segments between points on a line GeometryOperations

Express counts of dots, lines, faces Operations

Systematically count all triangles in a composite Geometry