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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 = 5.6cm, AD = 1.4cm, AC = 7.2cm, and AE = 1.8cm
Solution
AB = 5.6cm, AD = 1.4cm, AC = 7.2cm, and AE = 1.8cm
`"AD"/"AB" =(1.4)/(5.6) = (7)/(28) = (1)/(4)`
`"AE"/"AC" =(1.8)/(7.2) = (2)/(8) = (1)/(4)`
⇒ `"AD"/"AB" = "AE"/"AC"`
∴ ΔADE ∼ ΔABC
⇒ ∠D = ∠B; ∠E = ∠C
But these are corresponding angles
Hence, DE || BC.
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