 Hello and welcome to the session, I am Asha and I am going to help you with the following question which says, A, B, C, D is a rhombus, show that diagonal is AC by 6 angle E as well as C and diagonal BD by 6 angle B as well as D. This is right, what we are given, so here we are given a rhombus, the four sides of a rhombus are equal therefore we have AB is equal to BC is equal to CD is equal to DA and we have to prove first the diagonal AC by 6 angle A and C that is these two angles are equal and these two angles are equal that is first we have to prove angle DAC is equal to angle BAC second angle BCA is equal to angle DCA also diagonal BC by 6 angle B as well as D, so third we have to prove that angle ABD is equal to angle CBD and lastly that angle ADB is equal to angle CDB, so let us now begin with the proof, now in triangle DAB triangle DCB by DA is equal to DC and this is given to us also AB is equal to BC, this is also given to us DB is equal to BT, this is common to both the triangles, two ends condition, angle DAB is concurrent to triangle DCB which further implies that angle ABD is equal to angle CBD angle ADB is equal to angle CDB and this is by CPCT that is corresponding parts of concurrent triangles are equal, so this implies diagonal BT by 6 angle B angle D, now let us consider the triangles ADC and triangle ABC, now in these two triangles side AC is equal to CA this is common to both the triangles side AD is equal to AB, this is given since it is a rhombus all the four sides are equal and DC is equal to BC again since this is given to us, therefore by SSS congruence condition we can say that both the triangles are congruent that is triangle ADC is concurrent to triangle ABC which further implies angle DAC is equal to angle BAC and angle DCA is equal to angle BCA, so this is by CPCT that is corresponding parts of congruent triangles are equal and this implies that diagonal AC bisects angle A as well as angle C, so this completes the session hope you enjoyed it take care and have a good day.