In Figure, `A B C D` is a trapezium in which `A B C D` and `A D=B Cdot` show that : `/_A=/_B` (ii) `/_C=/_D` ` A B C~= B A D` diagonal `A C=d i agon a lB D`
In Figure, `ABCD` is a trapezium in which`ABCD \and\,AD=BC`

Explanation

In Figure, `ABCD`
is a trapezium in which`ABCD \and\,AD=BC`,
`/_A=/_B`(ii)
`/_C=/_D`(sum of adjacent angles in parellogram is `pi`
`/_D/_C+180^0--2x=180^0`
`/_C+/_D=2x`
`/_B+/_C=180^0`
`180^0-x+/_C=180^0`
`/_C+/_D=2x`
`/_B+/_C=180^0`
`180^0-x+/_C=180^0=0`
`/_C=/_D=x`
Hence Proved.
`/_\ABC=/_\BAD`(side AB is common)
`AD=BC`(given)
So, the angles including both the sides is also same
`/_A=/_B`
`/_\ABC=/_\BAD`(By SAS Congruent rule)
Hence Proved.
The third side of both triangle i.e.digonals are equal `AC=BD`