Geometry
Lines and angles168 problems · 12 skills
Angle chasing 16Angles in isosceles triangles 17🔒Angles in parallelograms 13🔒Angles in quadrilaterals 18🔒Angles of a quadrilateral 18🔒Angles on parallel and straight lines 7🔒Complementary and supplementary angles 18🔒Exterior angles 9🔒Obtuse and isosceles angles 17🔒Points and segments on a line 9🔒Reflections of light 9🔒Triangle angles in a ratio 17🔒
Triangles155 problems · 10 skills
Altitudes 14Altitudes and Heron's formula 17🔒Base and height 17🔒Distances in equilateral triangles 16🔒Equilateral triangles 16🔒Integer-sided triangles 18🔒Isosceles triangle properties 17🔒Isosceles triangles 17🔒Perimeters in configurations 12🔒Smallest integer figures 11🔒
Right triangles and Pythagoras113 problems · 9 skills
30-60-90 triangles 1045-45-90 triangles 3🔒Altitudes and tangent circles 18🔒Area and perimeter of right triangles 18🔒Isosceles right triangles 7🔒Poles and ropes 17🔒Pythagoras: the missing side 18🔒Pythagorean triples 17🔒Right triangles in figures 5🔒
Quadrilaterals217 problems · 15 skills
Area of a parallelogram 18Area of a trapezium 16🔒Diagonals of squares and rectangles 17🔒Folding paper 9🔒General quadrilaterals 17🔒Kites 7🔒Lengths in squares and rectangles 18🔒Midpoints in quadrilaterals 13🔒Perimeter of a parallelogram 17🔒Points inside a square 5🔒Quadrilaterals from diagonals 12🔒Rhombus: angles and sides 18🔒Rhombus: area and diagonals 17🔒Squares: midpoints and rotations 17🔒Trapezium midlines and diagonals 16🔒
Polygons113 problems · 9 skills
Angles in pentagons 10Area ratios in hexagons 9🔒Areas in hexagons 12🔒Hexagon angles and sides 9🔒Interior angle sum 17🔒Octagons 14🔒Pentagons 13🔒Regular hexagons 11🔒Regular polygon angles 18🔒
Area and perimeter225 problems · 18 skills
Area of a rectangle 12Comparing perimeters 14🔒Cost of floors and fields 2🔒Fencing costs 2🔒Frames and borders 7🔒Paths in plots 12🔒Percentage change in area 17🔒Perimeter of a rectangle 14🔒Rectangle from perimeter and area 18🔒Rectangle sides from a ratio 18🔒Rectangles cut into squares 4🔒Rectangles in proportion 15🔒Rectangles with changed sides 18🔒Shaded areas in squares 16🔒Similar rectangles 7🔒Square side and perimeter 18🔒Tiling a floor 15🔒Triangles inside rectangles 16🔒
Circles: area, arcs and sectors196 problems · 17 skills
Arc length 13🔒Area and circumference 18🔒Belts and gaps 3🔒Bending wire into shapes 12🔒Circles in squares 15🔒Comparing circle areas 5🔒Grazing goats 10🔒Perimeters of inscribed figures 8🔒Radius from area and circumference 18🔒Rings and paths 7🔒Sectors and arcs 17🔒Segments and chords 9🔒Semicircles 12🔒Shaded regions with circles 4🔒Squares and circles 12🔒Tangent circles 15🔒Wheels and revolutions 18🔒
Chords, tangents and inscribed angles96 problems · 7 skills
Angles in circles 16🔒Angles in cyclic quadrilaterals 9🔒Chord and distance from the centre 18🔒Chord lengths 9🔒Cyclic quadrilaterals 12🔒Tangents from a point 18🔒Trapezia in circles 14🔒
Medians, bisectors and triangle centres156 problems · 10 skills
Angle bisector ratios 17🔒Angle bisectors 18🔒Area ratios with circles 16🔒Areas with medians and midpoints 18🔒Cevians and midsegments 5🔒Circles touching a triangle 17🔒Incircle, excircle and circumcircle 18🔒Inradius and circumradius 18🔒Length of a median 17🔒Orthocentre and reflections 12🔒
Similarity and ratios95 problems · 7 skills
Area ratios with cevians 17🔒Dividing a segment in a ratio 9🔒Heights from shadows 16🔒Parallel lines in a triangle 16🔒Ratios of sides and perimeters 18🔒Similar figures: area ratios 17🔒Similar right triangles 2🔒
Scale drawings and real-world geometry48 problems · 3 skills
Geometric maximum and minimum91 problems · 8 skills
Extremes in a square 13🔒Extremes in a triangle 17🔒Extremes on a line 10🔒Largest areas in a circle 7🔒Largest right triangle 14🔒Largest shapes inside a triangle 6🔒Shortest paths 11🔒Smallest triangle 13🔒