Questions
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.
detailed solution
1
Steps of construction:
Proof:
In ΔBB₃C', B₂C || B₃C',
Hence,
B₂B₃/BB₂ = CC'/BC = 1/2
Adding 1 to CC'/BC = 1/2
CC'/BC + 1 = 1/2 + 1
(BC+CC')/BC = 3/2
BC'/BC = 3/2
Consider ΔBAC and ΔBA'C'
∠ABC = ∠A'BC' (Common)
∠BCA = ∠BC'A' (Corresponding angles ∵ CA || C'A')
∠BAC = ∠BA'C' (Corresponding angles)
By AAA axiom, ΔBAC ~ ΔBA'C'
∴ Corresponding sides are proportional
Hence,
BA'/BA = BC'/BC= C'A'/CA = 3/2
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