Question -
Answer -
Given : Lines AB and CD intersect each other at O.
OE and OF are the bisectors of тИаAOC and тИаBOD respectively
┬а
To prove : OE and OF are in the same line
Proof : тИ╡ тИаAOC = тИаBOD (Vertically opposite angles)
тИ╡ OE and OF are the bisectors of тИаAOC and тИаBOD
тИ┤ тИа1 = тИа2 and тИа3 = тИа4
тЗТ тИа1 = тИа2 =┬а
┬атИаAOC and тИа3 = тИа4 =┬а┬атИаBOD тИ┤ тИа1 = тИа2 = тИа3 = тИа4
тИ╡ AOB is a line
тИ┤ тИаBOD + тИаAOD = 180┬░ (Linear pair)
тЗТ тИа3 + тИа4 + тИаAOD = 180┬░
тЗТ тИа3 + тИа1 + тИаAOD = 180┬░ (тИ╡ тИа1 = тИа4)
тИ┤ EOF is a straight line