Mathematics
In the following figure, l // m // n. If OC = OD = 5 cm, OA = 8cm and OE = 10 cm, find OB and OF.
Mid-point Theorem
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Answer
In Δ OAC and Δ OBD,
∠AOC = ∠DOB (Vertically opposite angles)
∠OCA = ∠ODB (Alternate angles of parallel lines)
∠OAC = ∠OBD (Alternate angles of parallel lines)
By AAA rule,
Δ OAC ~ Δ OBD
Thus,
⇒
⇒
⇒ OB = 8 cm
Similarly, in Δ OEC and Δ OFD,
∠EOC = ∠DOF (Vertically opposite angles)
∠OCE = ∠ODF (Alternate angles of parallel lines)
∠OEC = ∠OFD (Alternate angles of parallel lines)
By AAA rule,
Δ OEC ~ Δ OFD
Thus,
⇒
⇒
⇒ OF = 10 cm
Hence, OB = 8 cm and OF = 10 cm.
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