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प्रश्न
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles
उत्तर
In ΔABC, the coordinates of the vertices are A(–2, 0), B(2, 0), C(0, 2).
`AB = sqrt((2+2)^2 + (0 - 0)^2) = 4`
`BC = sqrt((0 - 2)^2 + (2 - 0)^2) =sqrt8 = 2sqrt2`
`CA = sqrt((0 + 2)^2 + (2 - 0)^2) = sqrt8 = 2sqrt2)`
In ΔPQR, the coordinates of the vertices are P(–4, 0), Q(4, 0), R(0, 4).
`PQ = sqrt((4+4)^2 + (0-0)^2) = 8`
`QR = sqrt((0 - 4)^2 + (4 - 0)^2) = 4sqrt2`
`PR= sqrt((0 + 4)^2 + (4 - 0)^2) = 4sqrt2`
Now, for ΔABC and ΔPQR to be similar, the corresponding sides should be proportional
So, `(AB)/(PQ) = (BC)/(QR) = (CA)/(PR)`
`=> 4/8 = (2sqrt2)/(4sqrt2) = (2sqrt2)/(4sqrt2) = 1/2`
Thus, ΔABC is similar to ΔPQR
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