Mathematics
In △ ABC, D is mid-point of AB and E is mid-point of BC. Calculate :
(i) DE, if AC = 6.4 cm,
(ii) ∠DEB, if ∠ACB = 63°.
Mid-point Theorem
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Answer
(i) By the Midpoint Theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of its length.
In △ ABC, since D is mid-point of AB and E is mid-point of BC.
So, DE = AC
DE = x 6.4 = 3.2 cm
Hence, the length of DE = 3.2 cm.
(ii) Since DE is parallel to AC (by mid-point theorem),
∠DEB = ∠ACB = 63° (∵ corresponding angles of parallel lines)
Hence, ∠DEB = 63°.
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