Question

征集初中阶段几何学里面用面积法解决问题的大量例题.

Answer 1

1.RT△ABC中∠C=90° AC=3 BC=4 求高CD

解;y由勾股定理得 AB=5

S△ABC =AC×BC/2=AB×CD/2 ∴CD=AC×BC/AB=12/5

2.△ABC中,AB=AC=10,BC=16 求高BD

作高AE 则BE=CE=8 由勾股定理得AE=6

S△ABC =AE×BC/2=AC×BD/2 ∴BD=AE×BC/AC=9.6

3..△ABC中,AB=AC BD为高 P是BC上任一点.PE⊥AC于E,PF⊥AB于F

求证：PE+PF=BD

证明：连AP 则S△ABC=S△APC+△APB=AC*PE/2+AB*PF/2=AC(PE+PF)/2

=AC*BD/2

∴PE+PF=BD