# 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 - Mathematics

#### 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

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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.