Question

class 9 maths ch 8 theorem 8.6​

Answer 1

HELLO DEAR,

Theorem 8.6

The diagonals of a parallelogram bisect each other.

Given: ABCD is a parallelogram with

AC and BD diagonals and O is

the point of intersection of AC

and BD.

To Prove: OA= OC and OB=OD.

Proof: since, opposite sides of

parallelogram are parallel.

AD ।। BC

with transversal BD

ang(ODA)= ang(OBC)

( Alternate interior angles)

AD ।। BC

with transversal AC

ang(OAD)= ang(OCB)

(Alternate interior angles)

In ∆AOD & ∆BOC

<OAD = <OCB (from above substitution)

AD = CB (opposite sides of llgram are equal)

<ODA = <OBC (from above substitution)

∆AOD ≅ ∆BOC (by ASA)

so,

OA = OC and OB = OD. (by CPCT)

I HOPE IT'S HELP YOU DEAR,

THANKS.

Answer 2

Step-by-step explanation:

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