Question

Is $\Delta CEG$ an isosceles triangle ?

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient
  

Answer 1

Answer: (A)

An isosceles triangle is a triangle that has two sides of equal length.

As given, $\angle EAC=\angle FAC$

In triangle AFG & triangle AEC,

$\angle EAC=\angle FAC$

$\angle F=\angle AEC={90}^o$

So, $\angle AGF=\angle GCE$

So, in triangle AFG & triangle GEC,

$\angle AGF=\angle EGC=\angle GCE$

So, in triangle GEC,

$\angle EGC=\angle GCE$

So, it has two sides of equal length.triangle GEC is isosceles triangle .