Question

Prove that angles opposite to equal sides of an isosceles triangle are equal

Answer 1

$\Huge\mathfrak{Solution}$


Given ABC is a isosceles triangle means AB = AC


$\mathbf{To prove : ∠C = ∠D}$


construction : Draw a bisector of ∠ A intersection BC at D


$\mathbf{Proof: }$


In ∆ BAD and ∆CAD


$\mathbf{AB = AC (given)}$


$\mathbf{∠BAD = ∠ CAD (By construction)}$


$\textbf{AD = AD ( common)}$


∆ BAD ≅ ∆CAD (by SAS Congruence criteria)



Thus


∠ABD = ∠ ACD ( By CPCT)


∠B = ∠C


proved


Thanks


Have a colossal day ahead


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