Q) In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY.

Ans: Since XZ ǁ BC, Therefore, *(BPT Theorem)*

∴ ………….. (i)

Since XZ ǁ BC, ∴ XY ǁ BM

∠ AXY = ∠ ABM (Corresponding angles)

∠ XAY = ∠ BAM (Common angle)

∴ Δ AXY Δ ABM (by AA property)

∴

Substituting value from equation (i), we get:

or XY = = 1.8

**Therefore, the value of XY is 1.8 cm.**