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.