In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that:

(i) ∆APC and ∆BPD are similar.

(ii) If BD = 2.4 cm, AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and PC.

In the given figure, AB || DC, BO = 6 cm and DQ = 8 cm; find: BP x DO.

Given: ∠GHE = ∠DFE = 90°, DH = 8, DF = 12, DG = 3x – 1 and DE = 4x + 2.

Find: the lengths of segments DG and DE.

In △PQR, ∠Q = 90° and QM is perpendicular to PR. Prove that :

(i) PQ² = PM × PR

(ii) QR² = PR × MR

(iii) PQ² + QR² = PR²