Question

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Answer 1

2) The sides opposite to equal angles of a triangle are equal. Prove that if two angles of a triangle are congruent, then the triangle is isosceles

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Answer 2

$\huge\mathbb\red{Question2:-}$

$\huge{\underline{\underline{Given→}}}$

$\sf\green{AB \: = \: AC}$

$\sf\green{∠\: B \: = \: ∠\: C}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:In\:∆ABD \: and \: ∆ACE }} }\\ \\\end{gathered}\end{gathered}$

• AB = AC

∠BAD = ∠ CAE

∠BDA = ∠ CEA

$\sf\blue{∆ABD\: ≈\:∆ACE}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: By \: AAS /: rule }} }\\ \\\end{gathered}\end{gathered}$

$\sf\blue{ BD \:=\: CE }$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: By \: CPCT }} }\\ \\\end{gathered}\end{gathered}$

diagram in attachment

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$\huge\mathbb\red{Question3:-}$

$\mathrm{\boxed{\boxed{\pink{→ Given ✔}}}}$

$\sf\blue{ A\: △ABC \:in \:which\: ∠B=∠C. }$

$\mathrm{\boxed{\boxed{\pink{→ To\: Prove✔}}}}$

$\sf\blue{ AB=AC}$

$\mathrm{\boxed{\boxed{\pink{→ Construction✔}}}}$

$\sf\blue{ Draw\: the\: bisector \:of\: ∠A \:and\: let\: it \:meet\: BC\: at\: D.}$

Proof :

In △s ABD and ACD,

∠B=∠C

∠BAD=∠CAD

AD=AD

So, by AAS criterion of congruence,

△ABD≅△ACD

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: ⟹\:AB\:=\:AC }} }\\ \\\end{gathered}\end{gathered}$

diagram in attachment

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