Answer: Both the pairs of triangles (a) and (b) are similar.
(a) By AA similarity statement.
(b) By proportionality statement.
Step-by-step explanation: We are given to check whether the pairs of triangles in cases (a) and (b) are similar or not.
(a) We see that in triangles ABC and PQR, we have
m∠A = m∠P = 41°, m∠B = m∠Q = 85° and m∠C = m∠R = 54°.
So, ΔABC and ΔPQR are similar by AA similarity statement.
(b) We see that in triangles ABC and DEF, we have
AB = 4, BC = 5, CA = 3, DE = 24, EF = 30 and FD = 18.
So, we have
![\dfrac{DE}{AB}=\dfrac{EF}{BC}=\dfrac{FD}{CA}=6.](https://tex.z-dn.net/?f=%5Cdfrac%7BDE%7D%7BAB%7D%3D%5Cdfrac%7BEF%7D%7BBC%7D%3D%5Cdfrac%7BFD%7D%7BCA%7D%3D6.)
That is, the corresponding sides of two triangles are proportional.
Thus, ΔABC and ΔDEF are similar by proportionality statement.