Question -
Answer -
Given : In тИЖABC, AE is the bisector of vertical exterior тИаA and AE тИе BC
┬а
To prove : тИЖABC is an isosceles
Proof: тИ╡ AE тИе BC
тИ┤ тИа1 = тИаB (Corresponding angles)
тИа2 = тИаC (Alternate angle)
But тИа1 = тИа2 (тИ╡ AE is the bisector of тИаCAD)
тИ┤ тИаB = тИаC
тИ┤ AB = AC (Sides opposite to equal angles)
тИ┤ тИЖABC is an isosceles triangle