Geometry & Figures
45 problem types
Angle Facts in a Figure
A clock face is twelve equal 30-degree parts 4.MD.C.64.MD.C.7 · adapt
A straight line is 180 degrees 4.MD.C.7 · take
Adjacent angles of a parallelogram sum to 180 4.G.A.2 · adapt
Corresponding and alternate angles are equal 4.G.A.1 · adapt
Draw an auxiliary parallel line to find a bent angle 4.G.A.1 · adapt
Exterior angle sum of a regular polygon is 360 4.G.A.24.MD.C.7 · adapt
Perpendicular is half of a straight angle 4.G.A.14.MD.C.7 · take
Polygon angle sum via triangulation from a vertex 4.G.A.2 · adapt
Quadrilateral angles sum to 360 degrees 4.MD.C.7 · take
Small angles combine into larger angles 4.MD.C.74.MD.C.5 · take
Split a polygon into triangles to sum angles 4.MD.C.7 · take
Triangle angles sum to 180 degrees 4.MD.C.7 · take
Use the 180-degree line to find figure angles 4.MD.C.7 · take
Isosceles and Equilateral Angle Chaining
Chain isosceles base angles to find unknown angles 4.MD.C.74.G.A.2 · take
Isosceles triangle from a rectangle diagonal 4.G.A.24.MD.C.7 · adapt
Spot equal sides to build isosceles triangles 4.MD.C.74.G.A.2 · take
Two radii form an isosceles triangle; find angles 4.MD.C.74.G.A.2 · take
Use equilateral 60-degree angles and equal sides 4.G.A.24.MD.C.7 · take
Transformations Preserve Measures
Center of rotation stays fixed 4.MD.C.5 · take
Even number of flips returns original 4.G.A.3 · take
Flip across a line creates symmetry 4.G.A.3 · take
Flipping or turning digits forms new digits 4.G.A.3 · adapt
Folded angles are equal; chain to the unknown 4.MD.C.7 · take
Folding makes congruent corresponding angles 4.G.A.1 · adapt
Four 90-degree turns return original 4.MD.C.5 · take
Rotation preserves side lengths and angle measures 4.MD.C.7 · take
Quadrilateral Diagonal Properties
Diagonals of a parallelogram bisect each other 4.G.A.2 · adapt
Square diagonals are equal and perpendicular bisectors 4.G.A.24.MD.A.3 · adapt
Radius and Diameter Relationships
All radii in one circle are equal 3.MD.D.83.G.A.1 · adapt
Center to edge distance is the radius 3.MD.D.83.G.A.1 · adapt
Diameter is twice the radius 3.OA.C.73.G.A.1 · adapt
Find each radius and diameter from segments 3.OA.C.73.G.A.1 · adapt
Perimeter of shape joining circle centers 3.MD.D.83.OA.C.7 · adapt
Perimeter of shapes from tangent circles 3.MD.D.83.OA.C.7 · adapt
Perimeter splits into radius arcs and straight parts 3.MD.D.83.G.A.1 · adapt
Polygon side equals sum of two radii 3.MD.D.83.G.A.1 · adapt
Rectangle sides are multiples of the diameter 3.OA.C.73.G.A.1 · adapt
Segment through chained centers as radius multiples 3.OA.C.73.G.A.1 · adapt
Triangle side equals sum of two radii 3.MD.D.83.G.A.1 · adapt
Systematically Count Shapes in a Figure
Count all shapes hidden in a grid 1.G.A.23.OA.D.9 · take
Count all the rhombuses in a figure of small triangles 4.G.A.2 · take
Count segments between points on a line 4.G.A.13.OA.D.9 · take
Express counts of dots, lines, faces 4.OA.C.5 · take
Systematically count all triangles in a composite 4.G.A.2 · take