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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có BE và AD là 2 đường trung tuyến=>G là trực tâm
=>BG=\(\dfrac{2}{3}\)BE=\(\dfrac{2}{3}\).9cm =6 cm
và GD= \(\dfrac{1}{2}\)AG=\(\dfrac{1}{2}\).8cm =4cm
KL
![](https://rs.olm.vn/images/avt/0.png?1311)
1)
xét ΔAEK và Δ CEG có:
EA=EC(gt)
EG=EK(gt)
góc AEK= góc GEC( 2 góc đối đỉnh)
=> ΔAEK=ΔCEG(c.g.c)
=> AK=GC
cm tương tự ta có:ΔGDC=ΔIDB(c.g.c)
=> GC=BI
và AK=GC
=> AK=GC=BI
2)
theo câu a, ta có ΔAEK=ΔCEG(c.g.c)
=> góc EAK= góc ECG
=> AK//GC
theo câu a, ta có: ΔGDC=ΔIDB(c.g.c)
=> góc DGC= góc DIB
=> GC//BI
và AK//GC
=> AK//BI
3)
ta có: AD là đường trung tuyến ứng với cạnh BC của Δ ABC
BE là đường trung tuyến ứng với cạnh AC của ΔABC
=> giao của AD và BE là trọng tâm của ΔABC
=> G là trọng tâm của ΔABC
=> GA=2GD
mà GI=ID
=> GA=GI+ID=GI
ta có G là trọng tâm của ΔABC; BE là đường trung tuyến của ΔABC
=> BG=2GE
mà GE=EK
=> BG=GE+EK=GK
xét ΔGAK và ΔGIB có :
GA=GI(cmt)
GK=GB(cmt)
góc AGK= góc BGI(2 góc đối đỉnh)
=>ΔGAK=ΔGIB(c.g.c)
4)
ta có AD là đường trung tuyến của ΔABC
=> AD=3GD
hay DG=DA:3
ta có : BE là đường trung tuyến của ΔABC
=> GE=BE:3
5)
nếu CF là đường trung tuyến của ΔABC cắt AD tại G thì G là trọng tâm của tam giác ΔABC( tương tự như câu 4)
=> CG=2GF
NX: 3 đường trung tuyến của 1 tam giác cắt nhau tại 1 điểm. điểm này gọi là trọng tâm của tam giác đó
điểm này cách trung điểm của cạnh mà đoạn thẳng đi qua nó một khoảng =1/2 k/cách từ điểm đó đến đỉnh của tam giác mà đoạn thẳng đã đi nó
![](https://rs.olm.vn/images/avt/0.png?1311)
Theo tính chất đường trung tuyến ta có
\(\frac{AG}{AD}=\frac{GB}{BE}=\frac{2}{3}\)
\(\Leftrightarrow\frac{AG}{12}=\frac{GB}{9}=\frac{2}{3}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{AG}{12}=\frac{2}{3}\\\frac{GB}{9}=\frac{2}{3}\end{cases}\Rightarrow\orbr{\begin{cases}AG=8\left(cm\right)\\GB=6\left(cm\right)\end{cases}}}\)
Vì \(G\in BE\)
\(\Rightarrow BG+GE=BE\)
\(\Rightarrow GE=9-6=3\left(cm\right)\)
Vậy \(AG=8cm\) và \(GE=3cm\)
Bác lm dài thế >: t/c 3 đg trung tuyến áp dụng luôn cx đc mà.
Theo t/c 3 đường trung tuyến ta có :
\(AG=\frac{2}{3}AD=\frac{2}{3}.12=\frac{24}{3}=8\left(cm\right)\)
\(GE=\frac{1}{3}BE=\frac{1}{3}.9=\frac{9}{3}=3\left(cm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
BC=căn 8^2+6^2=10cm
=>AD=5cm
AG=2/3*5=10/3cm
GD=5-10/3=5/3cm
![](https://rs.olm.vn/images/avt/0.png?1311)
1: Xét ΔABC có
AD là đường trung tuyến
BE là đường trung tuyến
AD cắt BE tại G
Do đó: G là trọng tâm của ΔABC
Suy ra: GA=2GD; GB=2GE
mà GI=2GD
nên GA=GI
Ta có: GB=2GE
mà GK=2GE
nên GB=GK
Xét tứ giác ABIK có
G là trung điểm của AI
G là trung điểm của BK
Do đó: ABIK là hình bình hành
Suy ra: AK=BI
2: Sửa đề; AK//CG
Xét tứ giác AGCK có
E là trung điểm của AC
E là trung điểm của GK
Do đó: AGCK là hình bình hành
Suy ra: AK//CG
3: Xét ΔGAK và ΔGIB có
GA=GI
GK=GB
AK=IB
Do đó: ΔGAK=ΔGIB
4: Ta có: G là trọng tâm của ΔABC
mà AD là đường trung tuyến
nên DG=DA/3
Ta có: G là trọng tâm của ΔABC
mà BE là đường trung tuyến
nên EG=BE/3
![](https://rs.olm.vn/images/avt/0.png?1311)
Giải:
a) Ta có: \(AG=\frac{2}{3}AD\Rightarrow\frac{1}{2}AG=\frac{1}{2}.\frac{2}{3}AD\Rightarrow IG=\frac{1}{3}AD\)
\(GD=\frac{1}{3}AD\) ( tính chất đường trung tuyến )
\(\Rightarrow IG=GD\)
\(GB=\frac{2}{3}BE\Rightarrow\frac{1}{2}GB=\frac{1}{2}.\frac{2}{3}BE\Rightarrow KG=\frac{1}{3}BE\)
\(GE=\frac{1}{3}BE\) ( tính chất đường trung tuyến )
\(\Rightarrow GE=KG\)
Xét \(\Delta IKG,\Delta DEG\) có:
IG = GD ( cmt )
\(\widehat{IGK}=\widehat{EGD}\) ( đối đỉnh )
\(GK=GE\) ( cmt )
\(\Rightarrow\Delta IKG=\Delta DEG\left(c-g-c\right)\)
\(\Rightarrow IK=DE\) (
\(\Rightarrow\widehat{IKG}=\widehat{GED}\) ( góc t/ứng ) ( đpcm )
Mà 2 góc trên ở vị trí so le trong
\(\Rightarrow\)IK // DE ( đpcm )
b) Theo tính chất đường trung tuyến
\(\Rightarrow AG=\frac{2}{3}AD\left(đpcm\right)\)
Vậy...
Lời giải:
$G$ là trọng tâm tam giác $ABC$
Theo tính chất trọng tâm và đường trung tuyến thì:
$\frac{AG}{AD}=\frac{2}{3}$
$\Rightarrow 3AG=2AD$
$\Rightarrow 2(AD-AG)=AG$
$\Rightarrow 2DG=AG\Rightarrow \frac{DG}{AG}=\frac{1}{2}$
$\frac{BG}{BE}=\frac{2}{3}$
$\Rightarrow \frac{BE-GE}{BE}=\frac{2}{3}$
$\Rightarrow 1-\frac{GE}{BE}=\frac{2}{3}$
$\Rightarrow \frac{GE}{BE}=\frac{1}{3}$
$\Rightarrow \frac{BE}{EG}=3$
Hình vẽ:
![](data:image/png;base64,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)