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![](https://rs.olm.vn/images/avt/0.png?1311)
Bạn tự vẽ hình nhé
a) Xét tam giác Abc có
PN // BC ,PN = 1/2 BC (PN là dường trung bình)
mà PN trùng PF hay NF
Suy ra BC // NF
Mà BN // CF
Trong tứ giác BNFC có :
BC là cạnh đối của NF
BN là cạnh đối của CF
Suy ra tứ giác BNFC là hình bình hành (có các cạnh đối song song)
b)Ta có : PN = 1/2 BC (cm a)
mà NF = BC (hai cạnh đối của hình bình hành BNFC)
Suy ra PN = 1/2NF hay PN = NE = EF
Suy ra PN + NE = NE + EF hay PE = NF
Suy ra BC = PE
Xét tứ giác PECB có
hai cạnh đối BC = PE (cmt)
Mà BC // PN hay BC // PE
Suy ra tứ giác PECB là hình bình hành (hai cạnh đối bằng nhau và song song)
Suy ra EC // PB và EC = PB (hai cạnh đối)
Vì P là trung điểm của AB nên AP = PB và AP trùng PB
Suy ra EC // AP và EC = AP
Vậy tứ giác PAEC là hình bình hành
![](https://rs.olm.vn/images/avt/0.png?1311)
a, + △ABC△ABC vuông ở A nên theo định lí Pytago ta có: AB2+AC2=BC2AB2+AC2=BC2
Hay: 52+AC2=132⟹AC=1252+AC2=132⟹AC=12
+ E là trung điểm của AB nên AE=EB=AB2=52=2,5AE=EB=AB2=52=2,5
+ N là trung điểm của AC nên AN=CN=AC2=122=6AN=CN=AC2=122=6
+ △AEC△AEC vuông ở A nên theo định lí Pytago ta có: EC2=AE2+AC2=2,52+122=150,25⟹EC≈12.3EC2=AE2+AC2=2,52+122=150,25⟹EC≈12.3
+ △ANB△ANB vuông ở A nên theo định lí Pytago ta có: NB2=AB2+AN2=62+52=61⟹BN≈7,8NB2=AB2+AN2=62+52=61⟹BN≈7,8
+ Trong tam giác vuông, trung tuyến ứng với cạnh huyền bằng một nửa cạnh huyền nên AM=BC2=6,5AM=BC2=6,5
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét ΔABC vuông tại A và ΔDBE vuông tại D có
góc B chung
=>ΔABC đồng dạng với ΔDBE
=>AB/DB=AC/DE
=>AB*DE=AC*BD
b: BC=căn 18^2+24^2=30cm
BD=CD=30/2=15cm
ΔABC đồng dạng với ΔDBE
=>AB/DB=BC/BE=AC/DE
=>24/DE=30/BE=18/15=6/5
=>DE=20cm; BE=25cm
c: Xét ΔMAE vuông tại A và ΔMDC vuông tại D có
góc AME=góc DMC
=>ΔMAE đồng dạng với ΔMDC
=>MA/MD=ME/MC
=>MA*MC=MD*ME
d: MA/MD=ME/MC
=>MA/ME=MD/MC
=>ΔMAD đồng dạng với ΔMEC
Lời giải:
Áp dụng định lý Pitago:
$BC=\sqrt{AB^2+AC^2}=\sqrt{18^2+24^2}=30$ (cm)
$AM=\frac{BC}{2}=30:2=15$ (cm) (tính chất đường trung tuyến ứng với cạnh huyền thì bằng 1 nửa cạnh huyền)
$GM=\frac{1}{3}AM=\frac{1}{3}.15=5$ (cm)
$GA=\frac{2}{3}AM=\frac{2}{3}.15=10$ (cm)
Hình vẽ:
![](data:image/png;base64,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)