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A B C D is a parallelogram, if the two d...

`A B C D` is a parallelogram, if the two diagonals are equal, find the measure of `/_A B Cdot`

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Given: `ABCD` is a parallelogram.
`=>AB=CD` and `AD=BC`
Now,
In `/_\ABD` and `/_\ACB`,
`AD=BC`
`BD=AC`
`AB=AB`
`:./_\ABD~=/_\ACB`
`:./_BAD=/_ABC`
Now, `AD∥BC` and transversal `AB` intersects them at `A` and `B` respectively.
`:./_BAD+/_ABC=180^@`
`=>/_ABC+/_ABC=180^@`
`=>2/_ABC=180`
`=>/_ABC=90^@`
`therefore` The measure of `/_ABC` is `90^@`.
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