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