Question

Cho tam giac ABC
co AB=6cm ; AC=4cm, tren canh AB lay diem D , tren canh AC lay diem E sao cho AD= 2cm ; AE = 3cm
a) Chung minh tam giac ADE dong giang vs tam giac ACB
b) biet tam giac co dien tich la S , tinh die tich tam giac ADE

Answer 1

a)Ta có:\(\dfrac{AE}{AC}\)=\(\dfrac{2}{4}\)=\(\dfrac{1}{2}\)

\(\dfrac{AD}{AB}\)=\(\dfrac{3}{6}\)=\(\dfrac{1}{2}\)

nên:\(\dfrac{AE}{AC}\)=\(\dfrac{AD}{AB}\)

xét ΔADE và ΔACB có: \(\dfrac{AD}{AC}\)=\(\dfrac{AE}{AB}\)(CMT)

góc A chung

vậy ΔADE ∼ ΔACB(c.g.c)