1.  Diagonals of a trapezoid if you know sides and angles at the base  

diagonals trapezoid abcd

a , b     -  bases

c black , d black     -  legs

alpha orange , beta brown     -  angles  at the base

d1 blue , d2 blue     -  diagonals

 

Find the diagonal of a trapezoid using the law of cosines  (  ) :

diagonals trapezoid abcd F1

diagonals trapezoid abcd F2

 

Find the diagonal of a trapezoid if given all four sides  (  ) :

diagonals trapezoid abcd F3

diagonals trapezoid abcd F4

 

 

2.  Diagonals of a trapezoid using height  

diagonals trapezoid h

a , b     -  bases

c black , d black     -  legs

alpha orange , beta brown     -  angles  at the base

d1 blue , d2 blue     -  diagonals

h  - height

 

Find the diagonal of a trapezoid using height, angles at the base and sides  ( d1d2 ) :

diagonals trapezoid h F1

diagonals trapezoid h F2

diagonals trapezoid h F3

 

diagonals trapezoid h F4

diagonals trapezoid h F5

diagonals trapezoid h F6

 

 

3.  Diagonals of a trapezoid if you know other diagonal, angle between the diagonals and height or area or midsegment  

diagonals trapezoid m

a , b     -  bases

d1 blue , d2 blue     -  diagonals

alpha orange , beta brown     -  angles between the diagonals

h  - height

m12 red  - midsegment

A18 black  - areaof a trapezoid

 

Find the diagonal of a trapezoid if given other diagonal, angle between the diagonals and height or area or midsegment  (  ) :

 

diagonals trapezoid m F11    diagonals trapezoid m F21

diagonals trapezoid m F12    diagonals trapezoid m F22

diagonals trapezoid m F13    diagonals trapezoid m F23

* It is true in this case:

diagonals trapezoid m F3

 

 

4.  Diagonals of a trapezoid using formula for the sum of the squared diagonals   

diagonals trapezoid f

a black  - lower base

b black  - upper base

c black , d black     -  legs

d1 blue , d2 blue     -  diagonals

 

Formula for the sum of the squared diagonals   :

diagonals trapezoid f F1

 

Find the diagonal of a trapezoid using formula for the sum of the squared diagonals  (  ) :

diagonals trapezoid f F2

diagonals trapezoid f F3