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Question

In ΔABC,A=45, B=60 and C=75. The angles of the triangle formed by joining the mid-points of the sides of this triangle are


A
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B
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C
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D
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Solution

The correct option is B

Consider the figure below:

D, E and F are the mid-points of the sides BC, AC and AB respectively.

From the converse of mid-point theorem, we can say that

DEAB, DFAC and EFAB

Also, DE=AB2=AF, DF=AC2=AE and EF=AB2=BD

Thus, AFDE,FBDE and EFDC are parallelograms.

In ABC and DEF,
EDF=CAB=45 [Opposite angles of parallelogram, AFDE]
DEF=ABC=60 [Opposite angles of parallelogram, FBDE]
and EFD=ACB=75 [Opposite angles of parallelogram, EFDC]
Hence, the angles of the triangle formed by joining the mid-points of the sides of ABC are 45, 60, 75.


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