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Question

Show that ΔABC with vertices A(–2, 0), B(0, 2) and C(2, 0) is similar to ΔDEF with vertices D(–4, 0), F(4, 0) and E(0, 4). [CBSE 2017]

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Solution

In ΔABC, the coordinates of the vertices are A(–2, 0), B(0,2), C(2,0).

AB=0+22+2-02=8=22CB=0-22+2-02=8=22AC=2+22+0-02=4

In ΔDEF, the coordinates of the vertices are D(–4, 0), E(4, 0), F(0, 4).

DF=4+42+0-02=8FE=0-42+4-02=42DE=0+42+4-02=42

Now, for ΔABC and ΔDEF to be similar, the corresponding sides should be proportional.

So, ACDF=BCFE=ABDE48=2242=224212=12=12Since, the corresponding sides are proportional Therefore, given two triangles are similar.

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