UK Secondary (7-11)
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Drawing quadrilaterals with Properties (Investigation)
Lesson

We know that a quadrilateral is a polygon with $4$4 sides, this means that quadrilaterals also have $4$4 interior angles. The other known fact we have is the the sum of the interior angles of a quadrilateral is $360^\circ$360°.

There are a number of different types of quadrilaterals, and they all have specific properties.  

Properties of quadrilaterals

 


Parallelogram

  • Opposite sides in a parallelogram are parallel
  • Opposite angles in a parallelogram are equal
  • Opposite sides in a parallelogram are equal
  • Diagonals of a parallelogram bisect each other 

 

Rectangle

  • Opposite sides in a rectangle are parallel
  • Opposite sides in a rectangle are equal
  • Diagonals of a rectangle bisect each other 
  • Diagonals in a rectangle are equal 

 

Square

  • All sides of a square are equal
  • Opposite sides in a square are parallel
  • Diagonals of a square are perpendicular to each other (cross at 90°)
  • Diagonals of a square bisect the angles at the vertices (makes them 45°)
  • Diagonals of a square bisect each other 
  • Diagonals of a square are equal 

 

Rhombus

  • Opposite angles of a rhombus are equal
  • Opposite sides in a rhombus are parallel
  • All sides of a rhombus are equal
  • Diagonals of a rhombus bisect each other at 90 degrees 
  • Diagonals of a rhombus bisect corner angles 
  • Diagonals of a rhombus bisect each other

 

Trapezium

  • An isosceles trapezium (trapezoid) has 2 pairs of adjacent angles equal
  • A trapezium (trapezoid) has one pair of opposite sides parallel
  • An isosceles trapezium (trapezoid) has one pair of opposites sides equal
  • Diagonals of an isosceles trapezium (trapezoid) are equal

 

Kite

  • A kite has 2 pairs of adjacent sides equal
  • A kite has 1 pair of opposite angles equal
  • The longest diagonal of a kite bisects the angles through which it passes 
  • Diagonals of a kite are perpendicular to each other 
  • The longest diagonal of a kite bisects the shorter diagonal

 

Remember!

Bisect means to cut something into two equal parts. If you bisect a line, you cut it into two right in the middle.

Let's explore what kind of criteria we need to be explicitly given to be able to draw a unique quadrilateral.

I'll start by asking you some questions, see if from the criteria I give you if you can draw 1, none or many quadrilaterals.

Question 1

Draw a quadrilateral with 2 sides of 4 cm, and 2 sides of 5 cm.

What kinds of quadrilaterals could you draw? How many different types?

 

Question 2

Draw a quadrilateral with with 1 pair of congruent sides, and 1 pair of parallel sides. What type is it?  Are their many different quadrilaterals that fit this criteria?

What about with 2 pairs of congruent sides and 2 pairs of parallel sides?  

  • What type of quadrilateral is this one? 
  • Are their many different quadrilaterals that fit this criteria?

 

Question 3

Draw a quadrilateral with 2 right angles, 1 set of parallel lines and 2 sets of perpendicular lines. 

  • What type of quadrilateral is this?  
  • Are there more than one type that fit this criteria?

 

Question 4

Draw a quadrilateral with no right angles and 2 sets of congruent sides of length 5 cm and 8 cm respectively.

  • What type of quadrilateral is this?  
  • Are there more than one type that fit this criteria?

 

Question 5

Draw a quadrilateral with no right angles, 2 pairs of parallel lines, with at least one length of exactly 5 cm.

  • What type of quadrilateral is this?  
  • Are there more than one type that fit this criteria?

 

Question 6

Draw a quadrilateral with no right angles, no parallel lines and no congruent lines. 

  • What type of quadrilateral is this?  
  • Are there more than one type that fit this criteria?

 

Question 7

Draw a quadrilateral with side lengths 3, 5, 6 and 10 cm.  

  • What type of quadrilateral is this?  
  • Are there more than one type that fit this criteria?

 

 

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