Question

ABCD is a parallelogram. X and Y are the midpoints of the side AD and BC respectively. Prove that CX and AY trisect the Diagonal DB.

Answer 1

Answer:

left part is first and right part is second

Answer 2

CX and AY trisect the diagonal BD

GIVEN

ABCD is a parallelogram. X and Y are the midpoints of the side AD and BC respectively.

TO PROVE

CX and AY trisect the Diagonal DB.

SOLUTION

We can simply solve the above problem as follows;

It is given,

ABCD is a parallelogram.

AB || CD

AY || XC

And,

AD = BC (Opposite sides of a parallelogram)

So,

1/2 AD = 1/2 BC

So,

AX = YC

AXYC is a prallelogram

In ΔDAM

X is the midpoint of AD

NX || AY

By converse of Mid-point theorem

N is the mid-point of DM.

Therefore,

DN = MN (Equation 1)

So, XC and AY bisect DB

In ΔBNC

Y is the mid-point of BC

YM || CM

By converse of Mid-point theorem;

N is the mid-point of BM

Therefore,

BM = MN (Equation 2)

From equation 1 and 2

CX and AY trisect the diagonal BD

CX and AY trisect the diagonal BD Hence, Proved.

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