Question

If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:
AD = 5.7cm, BD = 9.5cm, AE = 3.3cm, and EC = 5.5cm

Answer 1

AD = 5.7cm, BD = 9.5cm, AE = 3.3cm, and EC = 5.5cm

`"AD"/"BD" = (5.7)/(9.5)` = 0.6

`"AE"/"EC" = (3.3)/(5.5) = (3)/(5)` = 0.6

⇒ `"AD"/"BD" = "AE"/"EC"`

∴ ΔADE ∼ ΔABC
⇒ ∠D  = ∠B; ∠E = ∠C
But these corresponding angles
Hence, DE || BC.