Geometry & Figures

90 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

Draw axis to split into congruent halves GeometryMeasurement & 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

Symmetry axis splits figure into congruent halves Geometry

Use congruence to find lengths for area GeometryMeasurement & data

Congruent figures have equal corresponding sides GeometryMeasurement & data

Fold or half-turn overlap reveals symmetry Geometry

Overlapping congruent shapes leave congruent leftovers Geometry

Symmetry axis or center bisects corresponding-point segment Geometry

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

Net and Solid Structure

A segment in the net is an edge of the solid Geometry

Adjacent faces in a net meet perpendicularly Geometry

Cut an edge to unroll the sides into one rectangle Geometry

Dashed edges in a sketch are hidden Geometry

Each prism face: 4 perpendicular, 1 parallel Geometry

Exposed faces depend on a cube's position GeometryMeasurement & data

Face, edge and vertex counts identify a prism GeometryExpressions

Face, edge and vertex counts identify a pyramid GeometryExpressions

Faces are bounded by edges joining vertices Geometry

In a prism net the two congruent faces are the bases Geometry

Opposite faces of a prism are parallel Geometry

Ribbon length matches parallel box edges GeometryMeasurement & data

Ribbon parallel to an edge is as long as that edge GeometryMeasurement & data

A cylinder seen from the front is its vertical cross-section Geometry

Find every point the line passes through Geometry

Find the matching lengths in a cylinder net Geometry

More faces means more vertices and edges Geometry

Surface Area and Volume of Solids

A submerged stone displaces its own volume Geometry

Build the prism from its top, front and side views Geometry

Count how many fit along each edge GeometryMeasurement & data

Same boxes, different stacking, different surface area Geometry

Volume needs every length in the same unit GeometryMeasurement & dataRatios

Work back from volume or surface area to a missing edge GeometryExpressions

Cutting a piece away removes that much volume Geometry

Get a cylinder's height or radius back from its surface area GeometryExpressions

Scaling every edge by ■ scales volume by ■ cubed Geometry

Surface area is the sum of every face Geometry

Surface area is the sum of every face Geometry

Volume is the base stacked to the height Geometry

Same height, radius times ●, volume times ● squared Geometry

Cube Stacks and Their Views

Height on a plan makes it a solid Geometry

Layer and position fix how many faces show Geometry

Per-cell counts give the front and side views Geometry

See the shape after cubes are removed Geometry

Spot the piece added onto a shape Geometry

The longest side sets the cube's edge GeometryNumber system

Find the cubes removed twice over Geometry

Start where the front and side views pin the count down Geometry