Geometry Crossword
Solve 18 clues spanning the essential vocabulary of geometry — from triangles and circles to the Pythagorean theorem and transformations. Complete each word correctly to unlock its encyclopedic definition.
How to Play
- Click a white cell to select it — click the same cell again to toggle Across/Down direction.
- Type a letter to fill the cell; the cursor advances automatically.
- Use arrow keys to navigate the grid; Tab jumps to the next word.
- Click a clue in the list to jump directly to that word.
- Press Check Answers to see correct (green) and wrong (red) cells.
- Reveal Word fills the current word (−50 pts penalty).
- Complete a word correctly to unlock its encyclopedic definition!
Building your crossword…
Geometry Vocabulary: Shapes, Angles, and Theorems
Geometry is the branch of mathematics concerned with the shapes, sizes, and properties of figures and spaces. Its vocabulary — from basic concepts like polygon and vertex to theorems like the Pythagorean theorem — is essential for architecture, engineering, physics, computer graphics, and higher mathematics.
Triangle
A polygon with three sides and three interior angles that always sum to 180°. Triangles are the simplest rigid polygon, used in structural engineering because a triangle cannot be deformed without changing a side length. Types include equilateral, isosceles, scalene, right, acute, and obtuse.
Pythagorean Theorem
In any right triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). This theorem has over 370 known proofs and is the foundation of distance calculations in geometry, navigation, and physics.
Circle
A perfectly round plane figure where every point on the boundary is equidistant from the center. Key measurements: circumference C = 2πr, area A = πr². The ratio of circumference to diameter always equals π ≈ 3.14159, the most famous mathematical constant.
Polygon
A closed figure with three or more straight sides. The interior angles of any polygon with n sides sum to (n − 2) × 180°. Regular polygons (equal sides and angles) include the equilateral triangle, square, regular pentagon, and regular hexagon.
Symmetry
A figure has symmetry if it looks the same after a transformation — reflection (line symmetry), rotation (rotational symmetry), or translation. Symmetry appears throughout nature, art, and architecture and is studied formally in the branch of mathematics called group theory.
Parallel and Perpendicular
Parallel lines lie in the same plane and never intersect (equal slopes). Perpendicular lines meet at exactly 90° (slopes are negative reciprocals). These relationships are fundamental to coordinate geometry, architectural drawing, and the Cartesian coordinate system.
Congruent vs. Similar
Congruent figures have the same size and shape — one can be superimposed exactly on the other (symbolized ≅). Similar figures have the same shape but possibly different sizes — angles are equal, sides are proportional (symbolized ~). Congruence theorems (SSS, SAS, ASA) prove triangles identical.
Angle Types
Acute angles measure less than 90°; right angles measure exactly 90°; obtuse angles measure between 90° and 180°; straight angles measure exactly 180°. Understanding angle types is fundamental to triangle classification, parallel line theorems, and polygon interior angle calculations.
Why Geometry Matters
Geometry is the oldest branch of mathematics, with roots in ancient Egypt and Greece. Modern applications span GPS navigation (spherical geometry), computer graphics (3D transformations), architecture (structural design), robotics (spatial reasoning), and medicine (medical imaging and surgical planning).
Every career in STEM, design, construction, and many others requires geometric thinking. Mastering geometry vocabulary is the foundation for algebra 2, trigonometry, calculus, and beyond.