#### Question

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

#### Solution

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

Is there an error in this question or solution?

Solution Show that Triangleabc, 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 Concept: Similarity of Triangles.