如图,AB=AC,P、O在AB、AC上,AP=PQ=QB=BC,则∠A大小为?
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如图,AB=AC,P、O在AB、AC上,AP=PQ=QB=BC,则∠A大小为?
![](http://img.wesiedu.com/upload/2/29/22967b73713972c941ff767a89d3b1df.jpg)
![](http://img.wesiedu.com/upload/2/29/22967b73713972c941ff767a89d3b1df.jpg)
![如图,AB=AC,P、O在AB、AC上,AP=PQ=QB=BC,则∠A大小为?](/uploads/image/z/16983440-8-0.jpg?t=%E5%A6%82%E5%9B%BE%2CAB%3DAC%2CP%E3%80%81O%E5%9C%A8AB%E3%80%81AC%E4%B8%8A%2CAP%3DPQ%3DQB%3DBC%2C%E5%88%99%E2%88%A0A%E5%A4%A7%E5%B0%8F%E4%B8%BA%3F)
有点小难度,参考了别的题目.
过点B作PQ的平行线,过点P作AB的平行线,两条平行线相交于点D,连接CD
∴四边形BQPD是平行四边形
∵QB = QP
∴平行四边形BQPD是菱形
∴PD=PQ = AP,
∠QBD = ∠QPD
∵PD//AB
∴∠CPD = ∠A = ∠QPD
∴∠A = ∠QBD
∵AC = AB,AP = BQ
∴△PDC≌△APQ
∴CD = PQ,∠AQP=∠PCD
∵AQ = QP
∴∠A = ∠AQP
∴∠A = ∠QBD = ∠PCD
∵PQ = PD=DB = BC
∴△DBC是等边三角形
∴∠DBC+∠DCB = 120°
∴3∠A + ∠DBC+∠DCB=180°
∴∠A = 20°
![](http://img.wesiedu.com/upload/e/de/ede33029d058f113526a38932dd033e8.jpg)
过点B作PQ的平行线,过点P作AB的平行线,两条平行线相交于点D,连接CD
∴四边形BQPD是平行四边形
∵QB = QP
∴平行四边形BQPD是菱形
∴PD=PQ = AP,
∠QBD = ∠QPD
∵PD//AB
∴∠CPD = ∠A = ∠QPD
∴∠A = ∠QBD
∵AC = AB,AP = BQ
∴△PDC≌△APQ
∴CD = PQ,∠AQP=∠PCD
∵AQ = QP
∴∠A = ∠AQP
∴∠A = ∠QBD = ∠PCD
∵PQ = PD=DB = BC
∴△DBC是等边三角形
∴∠DBC+∠DCB = 120°
∴3∠A + ∠DBC+∠DCB=180°
∴∠A = 20°
![](http://img.wesiedu.com/upload/e/de/ede33029d058f113526a38932dd033e8.jpg)
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