Right Triangle
A right triangle is a triangle with one angle equal to 90 degrees. It has special relationships between its sides and angles, making it essential in trigonometry and measurement. Real-life applications include designing ramps, ladders leaning against walls, and constructing buildings.
Isosceles Triangle
An isosceles triangle has two equal sides and two equal base angles. Its symmetry makes it important in art, architecture, and design.
Equilateral Triangle
All three sides and angles of an equilateral triangle are equal. It represents perfect symmetry and balance, often seen in tiling, engineering structures, and logo designs.
Scalene Triangle
A scalene triangle has no equal sides or angles. It represents irregularity and occurs frequently in natural structures like mountains and rocks.
Square
A square is a quadrilateral with four equal sides and right angles. It has strong symmetry, and its conceptual area and perimeter are widely used in tiling, frames, and design.
Rectangle
A rectangle has opposite sides equal and four right angles. It is widely used in construction, packaging, and architectural design.
Parallelogram
A parallelogram has opposite sides parallel and equal. It relates closely to rectangles and rhombuses and finds applications in geometry and physics, particularly in vectors.
Rhombus
A rhombus has all sides equal and opposite angles equal. Its diagonal properties make it important in kite design and decorative patterns.
Trapezoid
A trapezoid has one pair of parallel sides. Depending on its properties, it can be isosceles, right, or scalene. It is used in bridge structures and geometric designs.
Isosceles Trapezoid
An isosceles trapezoid has non-parallel sides equal, giving it visual symmetry. It appears in decorative structures and patterns.
Isosceles Trapezoid with Inscribed Circle
This trapezoid has a circle that touches all its sides. It represents an advanced geometric concept useful in problem-solving.
Trapezoid with Inscribed Circle
Here, a circle touches all four sides of a trapezoid. It highlights tangency conditions and design applications.
Kite
A kite has two pairs of adjacent equal sides. Its diagonal intersection properties are seen in aerodynamics, flying kites, and art.
Cyclic Quadrilateral
In a cyclic quadrilateral, all vertices lie on a circle. Opposite angles are supplementary, making it important in circle geometry.
Tangential Quadrilateral
A tangential quadrilateral has a circle touching all sides internally. It has the property of equal sums of opposite sides, often appearing in geometry problems.
General Quadrilateral
A quadrilateral with no special properties is classified based on its sides and angles. Such shapes are commonly found in everyday objects.
Regular Hexagon
A hexagon has six equal sides and angles. Its symmetry is seen in honeycombs, tiling, and architecture.
Regular Polygon
Regular polygons have equal sides and angles. They are used in floor patterns, bridges, and decorative structures.
Circle
A circle is defined as the set of points equidistant from a center. Its radius, diameter, and circumference concepts are used in wheels, clocks, and daily objects.
Sector of a Circle
A sector is the region enclosed by two radii and an arc. It is widely used in graphs and pie charts.
Segment of a Circle
A segment is the region between a chord and an arc. It has applications in civil design and engineering.
Cube
A cube is a solid with six equal square faces. Examples include dice, boxes, and blocks.
Rectangular Parallelepiped
This is a 3D solid with rectangular faces. It is important in packaging and construction.
Prism
A prism has two identical faces with other faces connecting them. It is used in optics and structural geometry.
Regular Tetrahedron
A tetrahedron is a pyramid with four triangular faces. It occurs in crystals and symmetrical structures.
Regular Pyramid
A pyramid has a polygonal base and an apex. The Egyptian pyramids are real-world examples.
Frustum of a Regular Pyramid
A truncated pyramid used in architecture, furniture design, and construction.
Rectangular Right Wedge
A wedge-shaped solid used in mechanical and engineering applications.
Platonic Solids
Platonic solids are five symmetrical 3D figures: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. They have historical and mathematical importance.
Right Circular Cylinder
A solid with two parallel circular bases connected by a curved surface. Examples include pipes, cans, and storage tanks.
Right Circular Cylinder with an Oblique Plane Face
A cylinder cut at an angle, used in mechanical and industrial parts.
Right Circular Cone
A cone has a circular base and a pointed apex. Ice cream cones and funnels are practical examples.
Frustum of a Right Circular Cone
A truncated cone used in lampshades, buckets, and decorative items.
Sphere
A sphere has all points equidistant from the center. Real-life spheres include balls, planets, and bubbles.
Spherical Cap
A portion of a sphere cut by a plane. Seen in domes and hemispheres.
Spherical Sector
A section of a sphere formed by two radii and an arc. Useful in 3D geometry.
Spherical Segment
The region between two parallel planes cutting a sphere. Used in construction and design.
Spherical Wedge
A portion bounded by two planes meeting at the center of a sphere. It has mathematical modeling uses.
Ellipsoid
An ellipsoid resembles a stretched sphere. Examples include planets and eggs.
Circular Torus
A torus is a donut-shaped figure. It is applied in physics, geometry, and engineering.
