Shikha Sharma

The construction of angles uses only a compass and straightedge to draw exact angles without a protractor. A 60° angle comes from an equilateral-triangle arc, a 120° from two such arcs, a 90° from perpendicular arcs, and 30° and 45° come from bisecting 60° and 90°. This article gives step-by-step methods, the examples, and which angles are constructible.

A convex shape is a shape where the straight line joining any two points inside it stays completely inside - equivalently, every interior angle of a convex polygon is less than 180°. This guide gives the one-line test, the properties, six worked examples, and the mistakes that make students misclassify a shape.

A reflex angle is any angle greater than 180° and less than 360° - the larger opening on the outside of an ordinary angle. This article defines the reflex angle, shows how to measure one with a standard 180° protractor using the 360° - θ rule, explains why 180° and 360° are excluded, and works through examples from clock hands.

A rectangular prism (also called a cuboid) is a 3D solid with 6 rectangular faces, 12 edges, and 8 vertices. Its volume is V = l × w × h (length × width × height), and its surface area is S = 2(lw + lh + wh).

In math, a plane is a perfectly flat, two-dimensional surface that extends infinitely in every direction and has no thickness. This article covers the plane definition in math, its properties, how three non-collinear points fix exactly one plane, how planes are named, the difference between parallel and intersecting planes, and six worked examples.

Hexagon is a six-sided closed two-dimensional polygon with six vertices and six interior angles. In a regular hexagon, all six sides are equal, all six interior angles are 120°, and the sum of interior angles is 720°. The area of a regular hexagon with side s is (3√3)/2s².

Lines in geometry are straight, one-dimensional paths that have no thickness and run on forever in both directions. This article sorts out the point–line–ray–segment family first, then walks through every type a student meets: horizontal, vertical, parallel, perpendicular, intersecting, transversal, and skew lines, each with a labelled diagram and worked examples.

Adjacent angles are two angles that share a common vertex, share a common side (arm), and do not overlap. They sit next to each other — the word adjacent comes from Latin adjacens, meaning "lying near". Adjacent angles can be any size; they don't have to add to a specific number.

An angle bisector is a ray, line, or segment that divides an angle into two equal smaller angles. This article covers the definition, the key properties, the compass-and-straightedge construction, the angle bisector of a triangle and the incenter, and six worked examples.

Supplementary angles add to 180°; complementary angles add to 90°. This article compares the two side by side, gives three worked examples (Quick, Standard, Stretch), explains the most common mistake, and offers the mnemonic that stops students mixing them up — Complementary forms a Corner, Supplementary forms a Straight line.

The main parts of a circle are the centre, radius, diameter, circumference, chord, arc, sector, segment, tangent, and secant, every one of them defined by its relationship to the single fixed centre point. This article names and explains each part with a labelled diagram, the formulas tied to them, six worked examples, and the common mistakes students make.

In geometry, adjacent means "next to each other" — sharing a common side, edge, or vertex. Adjacent angles share a vertex and a side but don't overlap. Adjacent sides in a polygon share a common vertex. Adjacent in a triangle (with respect to an angle) is the side touching the angle that isn't the hypotenuse.

A line segment is a part of a straight line bounded by two distinct endpoints, so it has a fixed, measurable length — unlike a line or a ray, which run on forever. This article covers the definition and notation, how a segment differs from a line and a ray, its properties, the distance formula for length, and six worked examples.

A 90 degree angle is a right angle: the exact quarter turn formed when two lines meet perpendicularly, marked with a small square instead of an arc. This article covers the definition, how to construct one with a compass and verify it with the 3-4-5 rule, where right angles hold up buildings, and six worked examples.

The diameter of a circle is the longest chord, passing through the centre, equal to twice the radius. Formula: d = 2r, or d = C/π from circumference, or d = 2√(A/π) from area. This article gives the three diameter formulas, three worked examples (Quick, Standard, Stretch), and the historical thread from Archimedes to modern usage.

Supplementary angles are any two angles whose measures sum to exactly 180°. The two angles can be next to each other (forming a straight line — a linear pair) or completely separate — what matters is the sum, not the position.

An isosceles acute triangle has two equal sides, two equal angles, and all three angles less than 90°. This article covers the definition, why both labels can hold at once, its properties, the area and perimeter formulas, six worked examples, and the common mistakes students make.

Geometric shapes split into 2D (flat, with length and width) and 3D (solid, with length, width, and height). 2D shapes group into polygons (triangles, quadrilaterals, regular and irregular) and non-polygons (circle, ellipse). 3D shapes group into polyhedra (prisms, pyramids, Platonic solids) and curved solids (sphere, cylinder, cone).

Complementary angles are any two angles whose measures sum to exactly 90°. The two angles can sit side by side (forming a right angle — a corner) or be drawn anywhere on the page — what matters is the sum. This article covers the definition, properties, the two types (adjacent vs non-adjacent), the right-triangle connection, three worked examples.

A rectangle is a quadrilateral with four right angles, opposite sides equal and parallel, and diagonals that are equal in length and bisect each other. This article covers every property of a rectangle by sides, angles, and diagonals, derives the area l × w, perimeter 2(l+w), and diagonal √(l² + w²) formulas, and works through six examples.