Question

prove that every diagonal of a Rhombus bisect the angles at the vertices

Answer 1

I think this is answer

Given: ABCD is a rhombus, AC is a diagonal 
Statement: line AB in congruent to line BC
Angle 1 is congruent to angle 3
Line BC is II AC, AB is II to CD 
<2 in congruent <3, <1 is congruent to <4
<1 is congruent to <2, <3 is congruent to <4
AC bisects 

Answer 2

In rhom. ABCD

In triangle aob and aod

Oa is common . Ad = ab

Od =ob [diag. Bisects each other

Aob=aod [sss]

Thus oad = angle oab cpct

Thus similarly ocd= angle ocb and apd = odc and abo = angle obc.

Fig draw rhom ABCD abd draw diagonal which intersect at o

.

Ab should be base of rhombus..

Hope it helps.