# If the diagonal of a parallelogram are equall then show that it is a rectangle

2
by sombirjangrs

2016-02-06T18:08:48+05:30
Let ABCD a  ||gm
: opposite sides eaqual AB=CD and AD=BC
AC=BD |given
AB=BA |common
Therfore triangle ACB is Congurrent to triangle BDA
<ACB = < BAD (1) | by cpct
AD || BC and transversal AB intersects thm
<BAD + <ABC =180 (2)| SUm of consecutive interrior angleson the same side of the transversal is 180 degree

FROM (1) and (2)
therfore <A= 90 degree and <b =90 degree
Similarly we can prove <c=90 degree and <D=90 degree

Therfore ABCD is A triangle

NOTE: < is used for ANGLE and ||gm for parallelogram and || for parallel

THANK YOU :)

dude...u r supposed to write ABCD is a rectangle...not a triangle
sorry by mistake'
i gota type alot fo this :P  ;)
chill...just told coz that guy might get confused
2016-02-06T18:23:45+05:30
Let the parallelogram be ABCD and AC and BD are its diagonals
AC=BD(given)
AD=BC(opp. sides of a parallelogram are equal)
CD=CD(common)
∴By SSS congruence rule