Question

in triangle DEF and triangle PQR where DE is 2cm ,EF is 3cm, angle DEF is 60 and PQ is 6cm ,QR is 9cm, and angle PQR is 60 show that these are similar triangle with the appropriate criteria​

Answer 1

ΔDEF is similar to ΔPQR by SAS similarity rule

Explanation:

• Two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional.

Given

ΔDEF, with details:

• DE = 2 cm, EF = 3 cm, ∠DEF = 60°

ΔPQR , with details:

• PQ = 6 cm, QR = 9 cm, ∠PQR = 60°

As we see, the ratio of corresponding sides is:

• DE/PQ = EF/QR ⇔ 2/6 = 3/9 = 1/3

And corresponding angles are:

• ∠DEF = ∠PQR = 60°

Therefore, ΔDEF is similar to ΔPQR by SAS similarity rule