Table of Contents

Last modified on August 3rd, 2023

A quadrilateral is a flat geometric shape having four straight sides and four vertices. It is a type of polygon.

The word ‘quadrilateral’ is derived from the Latin words ‘quadri’, meaning ‘four’, and ‘latus’, meaning ‘side’.

- Has four straight sides; if ABCD is a quadrilateral, AB, BC, CD, and DA are the four sides
- Has four vertices creating four angles; points A, B, C and D are the four vertices creating angles ∠ABC, ∠BCD, ∠CDA, and ∠DAB
- All four interior angles add up to 360°; so ∠ABC+ ∠BCD + ∠CDA + ∠DAB = 360°

**In a quadrilateral ABCD, find ∠BCD, if ∠ABC = 80°, ∠CDA = 110°, and ∠DAB = 100°.**

Solution:

As we know,

In quadrilateral ABCD, **∠ABC+ ∠BCD + ∠CDA + ∠DAB = 360°**, here ∠ABC = 80°, ∠CDA = 110°, and ∠DAB = 100°

80° + ∠BCD +110° + 100° = 360°

∠BCD = 360°- (80° + 110° + 100°)

∠BCD = 360° – 290°

∠BCD = 70°

There are six basic types of quadrilaterals: 1) rectangle, 2) square, 3) parallelogram, 4) rhombus, 5) trapezoid, and 6) kite.

Each one of them and their basic properties are given below:

It is a type of quadrilateral with all its interior angles measuring less than 180°. A convex quadrilateral has both its diagonals inside the closed figure.

Square, rectangle, rhombus, and trapezoid are examples of a convex quadrilateral.

It is a type of quadrilateral with at least one of its interior angles measuring greater than 180°. A concave quadrilateral has one of its diagonals outside the closed figure.

Dart or arrowhead is an example of concave quadrilateral.

It is a type of quadrilateral with four sides of equal length and four angles of equal measure.

Square is the only regular quadrilateral.

It is a type of quadrilateral having one or more sides of unequal length and one or more angles of unequal measure.

Trapezoid and Kite are examples of irregular quadrilateral.

It is a type of quadrilateral with no self-intersecting sides. It can be either convex or concave.

Square, rectangle, and dart are some examples of simple quadrilateral.

Also known as a crossed quadrilateral, it is a type of quadrilateral having self-intersecting sides. A complex quadrilateral is also known as a crossed quadrilateral, bow-tie quadrilateral, or butterfly quadrilateral.

Crossed trapezoid, crossed-square, and crossed-rectangle are some examples of complex quadrilateral.

- Rectangle-shaped objects – Books, tabletops, mobile phones, and TV screens.
- Square-shaped objects – Chessboard, wall clock, and a slice of bread.
- Parallelogram-shaped objects – Street and traffic sign, the structures on the neck of a guitar, and the United States Postal Service logo.
- Rhombus-shaped objects – Section of a baseball field, mirrors, earrings, and rings.
- Trapezoid-shaped objects – Handbags, popcorn tins, guitar-like dulcimer, and truss bridge supports.
- Kite-shaped objects – A flying kite, wall hanging, and earrings.

**Ans**. Yes, all trapezoids are quadrilaterals.

**Ans**. Yes, all parallelograms are quadrilaterals.

**Ans**. Yes, a kite is always a quadrilateral.

**Ans. **Yes, quadrilaterals are a four-sided polygon.

**Ans**. Yes, all rectangles are quadrilaterals.

**Ans**. No, all quadrilaterals are not rectangles.

**Ans**. No, all quadrilaterals are not squares.

Ans. Yes, a square is always a quadrilateral.

**Ans**. No, every quadrilateral is not a rhombus.

**Ans**. Trapezoid.

**Ans**. Parallelogram.

**Ans**. Parallelogram, rhombus and kite are three quadrilaterals with no right angles.

**Ans**. Rectangle.

**Ans**. Square.

**Ans**. Right trapezoid.

**Ans**. Rhombus.

**Ans**. Rectangle.

**Ans**. The quadrilaterals that have their diagonals perpendicular to each other are a square, a rhombus and a kite.

**Ans**. A square, an isosceles trapezoid, and a rectangle are quadrilaterals having congruent diagonals.

**Ans**. Yes, a diamond is a quadrilateral because it has four closed straight sides.

Last modified on August 3rd, 2023