CBSE Class 12-science Answered
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Asked by sdmbotch1123 | 23 Sep, 2023, 06:51: PM
Expert Answer
Figure shows two angles 
ABC and DEF so that their arms ar parallel. AB || DE and BC || EF .
ABC and DEF so that their arms ar parallel. AB || DE and BC || EF .Let BG and EH are bisectors of respective angles. When arms are parallel, then ABC = DEF .
ABC = DEF .Also their bisected angles also equal.
Let us extend bisector HE to meet BC at I as shown in figure.
HEF = GBC ( corresponding angles ) Since HEF = GBC , we also get GBC = EIC .
HEF = GBC , we also get GBC = EIC . Hence GB || EI or bisectors are parallel .
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Other possibility of two angles with their arms are parallel is shown in above figure.
AB || DE and BC || EF
Bisector of ABC is drawn and is extended so that it meets DE at H and futher extension meets the bisector of DEFat J .
ABC is drawn and is extended so that it meets DE at H and futher extension meets the bisector of DEFat J .If HBG = θ , then BGH = (180-2θ) because sum of interior angles between parallel line is 180.
HBG = θ , then BGH = (180-2θ) because sum of interior angles between parallel line is 180.Hence we get , BHG = EHJ = θ ( 
sum of angles of triangle is 180 )
BHG = EHJ = θ ( sum of angles of triangle is 180 )BGH = DEF = 180-2θ . Hence bisected angles DEI = FEI = 90-θ
DEI = FEI = 90-θHence EJH = 180 - (90-θ) - θ = 90o
EJH = 180 - (90-θ) - θ = 90o---------------------------------------------------------------------
Answered by Thiyagarajan K | 27 Sep, 2023, 07:59: PM
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