Question

(c) In the figure (3) given below, angle PQR = angle PRS. Prove that triangles PQR and PRS
are similar. If PR = 8 cm, PS = 4 cm, calculate PQ​

Answer 1

Answer:

PS =SR (sides opposite to equal angles are equal)

SR=4cm

Answer 2

In ∆PQR, and ∆PRS,

angle PQR = angle PRS (given)

and angle P = angle P (common)

∆PQR ~ ∆PRS (AA rule)

=> PQ/PR = QR/RS = PR/PS

Now, since PQ/PR = PR/PS

=> PQ/8 = 8/4

=> 4PQ = 64

=> PQ = 16 cm.