ABCD is a parallelogram on whose side BC a point P lies. It DP and AB are produced ahead then they meet at L. Then prove that

(i) (ii)

(i) In ΔDPC & ΔBPL,

∠DPC = ∠BPL |vertically opposite ∠s

In ||gm ABCD,

DC||AB or DC||AL,

⇒ ∠DCP = ∠LBP

ΔDPC~ΔBPL by AA Similarity Rule

Hence,proved.

(ii)In ΔPLB & ΔDLA,

∠L = ∠L |common angle

In ||gm ABCD, AD||BC or AD||BP,

⇒ ∠LPB = ∠LDC |corresponding angles

ΔPLB~ΔDLA by AA Similarity Rule

…(1)

Subtracting 1 from both sides of the above equation,

…(2)

Multiplying (1) & (2),

Or,

Hence, proved.