Mathematics
In the figure (ii) given below, O is the point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that OCD is an isosceles triangle.
Triangles
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Answer
∠OAD = ∠DAB - ∠OAB = 90° - 60° = 30°.
Similarly,
∠OBC = ∠CBA - ∠OBA = 90° - 60° = 30°.
⇒ ∠OAD = ∠OBC.
AD = BC (As sides of squares are equal).
OA = OB (As OAB is equilateral triangle).
∴ △OAD ≅ △OBC by SAS axiom.
We know that corresponding parts of congruent triangles are equal.
∴ OD = OC.
Hence, proved that OD = OC i.e. OCD is an isosceles triangle.
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