Q. 6 B5.0( 1 Vote )

Fill in the blanks so that the following statements are true:

D, E, F are respectively the mid-points of , , of ΔPQR. The correspondence DEF _____ is similarity.

Answer :

We have

Given: D is the midpoint of PQ PD = DQ = 1/2 PQ

But PD = DQ = FE [, F and E are also midpoints of PR and QR respectively]

So, EF = 1/2 PQ

Or …(i)

E is the midpoint of QR QE = ER = 1/2 RQ

But QE = ER = DF [, D and F are also midpoints of PQ and PR respectively]

So, DF = 1/2 RQ

Or …(ii)

F is the midpoint of PR PF = FR = 1/2 RP

But PF = FR = DE [, D and E are midpoints of PQ and QR respectively]

So, DE = 1/2 RP

Or …(iii)

Comparing equations (i), (ii) & (iii), we get

We can also arrange it as,

The correspondence DEF RPQ is a similarity by SSS theorem.

Thus, answer is RPQ.

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