Question

If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:
AB = 10.8cm, BD = 4.5cm, AC = 4.8cm, and AE = 2.8cm

Answer 1

AB = 10.8cm, BD = 4.5cm, AC = 4.8cm, and AE = 2.8cm
AD = AB - BD = 10.8 - 4.5 = 6.3cm

`"AD"/"AB" =(6.3)/(10.8) = (2)/(36) = (7)/(12)`

`"AE"/"AC" =(2.8)/(4.8) = (14)/(24) = (7)/(12)`

⇒ `"AD"/"AB" = "AE"/"AC"`
∴ ΔADE ∼ ΔABC
⇒ ∠D = ∠B; ∠E = ∠C
But these are corresponding angles
Hence, DE || BC.