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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 - CBSE Class 10 - 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

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.
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