Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, A = 70°, PR = 9 cm, P = 70° and PQ = 4.5 cm. Show that ΔABC ~ ΔPQR and state the similarity criterion.

Question

Philoid · Accepted Answer

We know that if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar (SAS criteria).

Here in the given triangles, ∠A = ∠P = 70° .

And AB/PQ = AC/PR

i.e. 6/4.5 = 6/9

⇒ 2/3 = 2/3

Hence ΔABC ~ ΔPQR.

SAS-similarity