Question

prove that the diagonals of a parallelogram bisect each other​

Answer 1

Step-by-step explanation:

GIVEN: A parallelogram ABCD , Its diagonals, AC & BD intersect at O.

TO PROVE: AO = CO & BO = DO

PROOF: First we prove that opposite triangles formed by diagonals are congruent.. like..

In tri AOB & tri COD

< A = < c ( alternate interior angles, formed by AB // CD)

< B = < D ( same reason)

& AB = CD ( opposite angles of parallelogram)

=> tri AOB congruent to tri COD ( by ASA congruence theorem)

=> AO = CO & BO = DO ( cpct)

PLS MARK AS BRAINLIEST!!

Answer 2

Step-by-step explanation:

Let consider a parallelogram ABCD in which AB||CD and AD||BC.

In ∆AOB and ∆COD , we have

∠DCO=∠OAB (ALTERNATE ANGLE)

∠CDO= ∠OBA. (ALTERNATE ANGLE)

AB=CD. (OPPOSITE SIDES OF ||gram)

therefore , ∆ AOB ≅ ∆COD. (ASA congruency)

hence , AO=OC and BO= OD. (C.P.C.T)

$\huge \rm{hope \: it \: helps \: you}$