in fig 12.21 ABC is an equilateral triangle.D is any point inside it on DC an equilateral triangle DEC is drawn, as shown in the figure DE = DC . prove that triangle BDC and triangle CDE are congruent
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Consider the triangle △ADB.
∠BAD=60∘ and ∠ABD<∠ABC⟹∠ABD<60∘
Now, in a triangle, side opposite larger angle is greater than the side opposite smaller angle.
Hence, as BD is opposite ∠BAD, AD is opposite ∠ABD and we saw that ∠ABD<∠BAD=60∘,
∴BD>AD
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