Question

The diagonals of a trapezium ABCD intersect at O. AB is parallel to DC. AB= 3cm and DC =6cm. If CO= 4cm and OB=3cm. Find AO and DO.

Answer 1

Answer:

SUBSTITUTE THE VALUES GIVEN!""::

Step-by-step explanation:

The diagonals form 4 triangles in the interior of the trapezium.  The two triangles that have the parallel sides of the trapezium as their bases, ABO and CDO, are similar triangles (regardless of the shape of the trapezium).  We will use this similarity to find AO and DO.

 

Side AO corresponds to side CO.  Side CO is 4 cm.  Because the triangles are similar, we have:

 

CO/CD = AO/AB

 

4/6 = AO/3

 

AO = 2 cm

 

Side BO corresponds to side DO.  Again, because the triangles are similar::

 

BO/AB = DO/CD

 

3/3 = DO/6

 

DO = 6 cm