Question -
Answer -
Given : In AABC, side BC is produced to D such that BD = BC
тИаA = 70┬░ and тИаB = 60┬░
┬а
To prove :
(i) AD > CD (ii) AD > AC
Proof: In тИЖABC,
тИаA = 70┬░, тИаB = 60┬░
But Ext. тИаCBD + тИаCBA = 180┬░ (Linear pair)
тИаCBD + 60┬░ = 180┬░ 3
тЗТ тИаCBD = 180┬░ тАУ 60┬░ = 120┬░
But in тИЖBCD,
BD = BC
тИ┤ тИаD = тИаBCD
But тИаD + тИаBCD = 180┬░ тАУ 120┬░ = 60┬░
тИ┤тИаD = тИаBCD =┬а
┬а= 30┬░ and in тИЖABC,
тИаA + тИаB + тИаC = 180┬░
тЗТ 70┬░ + 60┬░ + тИаC = 180┬░
тЗТ 130┬░ + тИаC = 180┬░
тИ┤ тИаC =180┬░- 130┬░ = 50┬░
Now тИаACD = тИаACB + тИаBCD = 50┬░ + 30┬░ = 80┬░
(i) Now in тИЖACB,
тИаACD = 80┬░ and тИаA = 70┬░
тИ┤ Side AD > CD
(Greater angle has greatest side opposite to it)
(ii) тИ╡ тИаACD = 80┬░ and тИаD = 30┬░
тИ┤ AD > AC