Monday, May 4, 2020

QUADRILATERALS



Quadrilateral just means "four sides"
(quad means four, lateral means side).
A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.
Properties:-A quadrilateral has:
  • four sides (edges)
  • four vertices (corners)
  • interior angles that add to 360 degrees:Quadrilateral Angles
  • Try drawing a quadrilateral, and measure the angles. They should add to 360°
  • Types of Quadrilaterals

    There are special types of quadrilateral:
    Types of Quadrilateral
Some types are also included in the definition of other types! For example a squarerhombus and rectangle are also parallelogramsSee below for more details.
Let us look at each type in turn:

The Rectangle

Rectangle
the little squares in each corner mean "right angle"
rectangle is a four-sided shape where every angle is a right angle (90°).
Also opposite sides are parallel and of equal length.

The Square

Square
the little squares in each corner mean "right angle"
square has equal sides (marked "s") and every angle is a right angle (90°)
Also opposite sides are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

The Rhombus

Rhombus
rhombus is a four-sided shape where all sides have equal length (marked "s").
Also opposite sides are parallel and opposite angles are equal.
Rhombus Diagonals
Another interesting thing is that the diagonals (dashed lines) meet in the middle at a right angle. In other words they "bisect" (cut in half) each other at right angles.
A rhombus is sometimes called a rhomb or a diamond.

The Parallelogram

Parallelogram
parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same).

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

The Kite

The Kite
Hey, it looks like a kite (usually).
It has two pairs of sides:
Each pair is made of two equal-length sides that join up.
Also:
  • the angles where the two pairs meet are equal.
  • the diagonals, shown as dashed lines above, meet at a right angle.
  • one of the diagonals bisects (cuts equally in half) the other.


... and that's it for the special quadrilaterals.

Using the chart below we can answer such questions as:
  • Is a Square a type of Rectangle? (Yes)
  • Is a Rectangle a type of Kite? (No)
Quadrilateral Classification

Complex Quadrilaterals

Oh Yes! when two sides cross over, we call it a "Complex" or "Self-Intersecting" quadrilateral, like these:
Complex Quadrilaterals
They still have 4 sides, but two sides cross over.

Polygon

A quadrilateral is a polygon. In fact it is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on.
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