题目内容
如图,将纸片⊿ABC沿着DE折叠压平,则( )
A.∠A=∠1+∠2 | B.∠A=(∠1+∠2) | C.∠A= (∠2-∠1) | D.∠A= ∠2-∠1 |
C
解:∵把△ABC纸片沿着DE折叠,点A落在四边形BCED内部,
∴∠1+∠2=180°-∠ADA′+180°-∠AEA′
=180°-2∠ADE+180°-2∠AED
=360°-2(∠ADE+∠AED)
=360°-2(180°-∠A)=2∠A,
即∠A=(∠2-∠1),
故选B.
∴∠1+∠2=180°-∠ADA′+180°-∠AEA′
=180°-2∠ADE+180°-2∠AED
=360°-2(∠ADE+∠AED)
=360°-2(180°-∠A)=2∠A,
即∠A=(∠2-∠1),
故选B.
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