a) Xét ΔBDC và ΔHBC, ta có:
$\widehat B =\widehat H = 90^o$
$\widehat C$ chung
$\Rightarrow ΔBDC \sim ΔHBC$ (g-g)
b) Vì $ΔBDC \sim ΔHBC$ (chứng minh trên)
$\Rightarrow\dfrac{BD}{HB} =\dfrac{DC}{BC} =\dfrac{BC}{HC}$
$\Rightarrow\dfrac{BD}{HB}= \dfrac{25}{15} =\dfrac{25}{HC}$
$\Rightarrow HC=\dfrac{15.15}{25} =9$ (cm)
Vì $H∈DC$
Nên $HD = DC - HC$
$\Rightarrow HD = 25 - 9=16$ (cm).