Question

12. Problem: Let OABC be a parallelogram and D the midpoint of OA. Prove that the segment CD
trisects the diagonal OB and is trisected by the diagonal OB.​

Answer 1

Answer:

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Answer 2

+1Answer:

It is a theorem. So lets prove it in detail in step by step.

Step-by-step explanation:

Let OA=a, OC=b so that Ob=a + b and OD =a/2

Let M be the point of trisection of OB and CD.

Let OM:MB=K:1 (say)

Let CM:MD= L:1 (say)

So, OM= K(a + b)+1(0)/K+1 = K(a + b)/K+1--------->EQUATION 1

and OM= L(a/2)+1(b)/L+1------------->EQUATION 2

We know these equations are equal . Therefore compare both the equations

L/2(L+1)=K(a + b)/K+1 = L(a/2)+b/L+1

We get l = 2 and k=1/2

Therefore CD trisects OB and OB trisects CD.

HENCE PROVED