Question

Answer 1

a) Ta có:
$\dfrac{AD}{AB}=\dfrac{1}{3}$

$\dfrac{AE}{AC}=\dfrac{2}{6}=\dfrac{1}{3}$

$\Rightarrow \dfrac{AD}{AB}=\dfrac{AE}{AC}$

b) Xét: $\dfrac{AD}{AB}=\dfrac{AE}{AC}$

Lại có $\widehat{DAE}=\widehat{BAC}$ (góc chung)

$\Rightarrow \triangle ADE \sim \triangle ABC$ (theo trường hợp c.g.c)

c) Từ $\triangle ADE \sim \triangle ABC$ suy ra:
$\dfrac{DE}{BC}=\dfrac{AD}{AB}$

$\Rightarrow DE=\dfrac{AD}{AB}\cdot BC=\dfrac{1}{3}\cdot4=\dfrac{4}{3}\text{ cm}$