"In geometry, a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices)."
This topic covers the different types of quadrilaterals (such as rectangles, squares, parallelograms, and trapezoids), their properties, and how to solve problems involving them.
Properties of quadrilaterals: This covers the basic characteristics of quadrilaterals, such as having four sides, four angles, and four vertices. It also includes their classification into various types and subtypes based on their properties.
Types of quadrilaterals: This covers the different types of quadrilaterals, such as squares, rectangles, parallelograms, trapezoids, rhombuses, kites, and cyclic quadrilaterals. It also includes the properties and formulas associated with each type.
Diagonals of quadrilaterals: This covers the properties and formulas associated with the diagonals of quadrilaterals, such as their length, intersecting point, and angle bisectors.
Congruent and similar quadrilaterals: This covers the concepts of congruence and similarity, and how they apply to quadrilaterals. It includes the properties and criteria for proving two quadrilaterals are congruent or similar.
Perimeter and area of quadrilaterals: This covers the formulas and methods for calculating the perimeter and area of different quadrilaterals, such as using side lengths, diagonals, angles, and the Pythagorean theorem.
Special properties of specific quadrilaterals: This covers the unique properties and formulas associated with specific types of quadrilaterals, such as the diagonals and area of a rectangle, the angle sum and side ratios of a parallelogram, and the diagonals and area of a rhombus.
Construction of quadrilaterals: This covers the methods for constructing different types of quadrilaterals using a ruler and compass, such as constructing a square, rectangle, parallelogram, and trapezoid.
Transformation of quadrilaterals: This covers the concepts of translation, rotation, reflection, and dilation, and how they apply to quadrilaterals. It also includes the properties and formulas associated with each type of transformation.
3D quadrilaterals: This covers the properties and formulas associated with quadrilaterals in 3D space, such as a parallelogram in a plane or a quadrilateral pyramid.
Real-world applications of quadrilaterals: This covers the real-world applications of quadrilaterals, such as designing buildings, creating maps, and calculating the perimeter and area of land parcels.
Square: A quadrilateral with equal sides and four right angles.
Rectangle: A quadrilateral with four right angles, opposite sides that are equal in length, and parallel.
Rhombus: A quadrilateral with equal sides, opposite angles that are equal, and diagonals that are perpendicular bisectors of each other.
Parallelogram: A quadrilateral with opposite sides that are parallel and equal in length.
Trapezoid: A quadrilateral with one pair of parallel sides and one pair of non-parallel sides.
Kite: A quadrilateral with two pairs of adjacent sides that are equal in length, and diagonals that are perpendicular to each other.
Isosceles Trapezoid: A trapezoid with equal base angles and equal non-parallel sides.
Quadrilateral: A four-sided polygon with no specific properties or restrictions.
"The word is derived from the Latin words quadri, a variant of four, and latus, meaning 'side'."
"It is also called a tetragon, derived from Greek 'tetra' meaning 'four' and 'gon' meaning 'corner' or 'angle'."
"A quadrilateral with vertices A, B, C, and D is sometimes denoted as ◻ABCD."
"Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed)."
"Simple quadrilaterals are either convex or concave."
"The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees of arc."
"∠A + ∠B + ∠C + ∠D = 360°."
"This is a special case of the n-gon interior angle sum formula: S = (n − 2) × 180°."
"All non-self-crossing quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges."
"The Latin word quadri means a variant of four."
"The Greek word 'tetra' means 'four'."
"The Latin word latus means 'side'."
"The Greek word 'gon' means 'corner' or 'angle'."
"Quadrilaterals are either simple or complex."
"Simple quadrilaterals are either convex or concave."
"The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees of arc."
"∠A + ∠B + ∠C + ∠D = 360°."
"All non-self-crossing quadrilaterals tile the plane."
"Quadrilaterals tile the plane by repeated rotation around the midpoints of their edges."