Question

梯形ABCD中,AB平分CD,AD=a,CD=b,AB=a+b,证明:角D等于2角B.

Answer 1

过D点作CB的平行线交AB于E点,则四边形DEBC是平行四边形,∴∠CDE＝∠B∴DC=EB=a,∴AE=a＋b－b=a,∴AD=AE,∠ADE=∠AED,又DC∥AB,∴∠CDE=∠AED=∠B ,∴∠ADC=∠ADE+∠CDE =2∠B