Question

如图,D是ΔABC的边BC上一点,AB=AC=CD,且AD=BD,试求∠B的大小

Answer 1

由题知ΔABC等腰,∠B=∠C=1/2(180-∠A)=90-1/2∠A;

因为ΔDAB等腰,有∠B=∠DAB=1/2∠ADC,又因ΔCAD等腰,故∠ADC=∠CAD,

于是∠B=∠DAB=1/2∠CAD,

而∠A=∠DAB+∠CAD=3∠DAB=3∠B

(∠CAD=2∠DAB,∠B=∠DAB)

由此可得∠B=90-1/2∠A=90-3/2∠B

移项得5/2∠B =90

解得∠B=32度