Cho tam giác ABC cân tại A,AB=4.Từ 1 điểm D trên cạnh BC vẽ DE//AB (E thuộc AC) và DF//AC (F thuộc AB) tính chu vi tứ giác AEDF
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
-Ta có: DE//AB, DF//AC (gt).
\(\Rightarrow\) AEDF là hình bình hành mà AD là tia phân giác của \(\widehat{BAC}\) (gt).
\(\Rightarrow\) AEDF là hình thoi.
-Xét △ABC có: DF//AC (gt).
\(\Rightarrow\dfrac{BF}{AB}=\dfrac{DF}{AC}\) (định lí Ta-let).
\(\Rightarrow1-\dfrac{DF}{AB}=\dfrac{DF}{AC}\)
\(\Rightarrow\dfrac{DF}{AB}+\dfrac{DF}{AC}=1\)
\(\Rightarrow DF.\left(\dfrac{1}{AB}+\dfrac{1}{AC}\right)=1\)
\(\Rightarrow DF.\left(\dfrac{1}{3}+\dfrac{1}{6}\right)=1\)
\(\Rightarrow DF.\dfrac{1}{2}=1\)
\(\Rightarrow DF=2\) (cm).
\(\Rightarrow P_{AEDF}=4.DF=4.2=8\left(cm\right)\) (do AEDF là hình thoi).
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AEDF có
\(\widehat{AED}=\widehat{AFD}=\widehat{FAE}=90^0\)
Do đó: AEDF là hình chữ nhật
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác AEDF có
\(\widehat{AED}=\widehat{AFD}=\widehat{FAE}=90^0\)
Do đó: AEDF là hình chữ nhật
b: Xét ΔABC có
D là trung điểm của BC
DE//AC
Do đó: E là trung điểm của AB
Xét tứ giác AIBD có
E là trung điểm của AB
E là trung điểm của ID
Do đó: AIBD là hình bình hành
mà AB\(\perp\)DI
nên AIBD là hình thoi
![](https://rs.olm.vn/images/avt/0.png?1311)
Xét tứ giác AEDF có
AE//DF
DE//AF
Do đó: AEDF là hình bình hành
mà \(\widehat{DAE}=90^0\)
nên AEDF là hình chữ nhật
![](https://rs.olm.vn/images/avt/0.png?1311)
a/
DE//AB=> DE//AF
DF//AC=>DF//AE
=> AEDF là hình bình hành (Tứ giác có các cặp cạnh đối // với nhau từng đôi một là hbh)
Hình bình hành AEDF có \(\widehat{A}=90^o\) => AEDF là hình chữ nhật
b/
DE//AB
DB=DC (1)
=> FA=FC (trong tg đường thẳng đi qua trung điểm 1 cạnh và // với 1 cạnh thì đi qua trung điểm cạnh còn lại (2)
Từ (1) và (2) => DE là đường trung bình của ABC
\(\Rightarrow DE=\dfrac{BC}{2}=FB=FC\) (3)
DE//AB=> DE//FB (4)
Từ (3) và (4) => BFED là hình bình hành (Tứ giác có cặp cạnh đối // và bằng nhau là hbh)
a) Do DE // AB (gt)
\(AC\perp AB\) (\(\Delta ABC\) vuông tại A)
\(\Rightarrow DE\perp AC\)
\(\Rightarrow\widehat{DEA}=90^0\)
Do DF // AC (gt)
\(AB\perp AC\) (\(\Delta ABC\) vuông tại A)
\(\Rightarrow DF\perp AC\)
\(\Rightarrow\widehat{DFA}=90^0\)
Tứ giác AEDF có:
\(\widehat{EAF}=\widehat{DEA}=\widehat{DFA}=90^0\)
\(\Rightarrow AEDF\) là hình chữ nhật
b) Do D là trung điểm BC (gt)
DF // AB (gt)
\(\Rightarrow F\) là trung điểm của AB
\(\Rightarrow FA=FB\)
Do AEDF là hình bình hành
\(\Rightarrow DE=AF\)
\(\Rightarrow DE=FB\)
Lại có:
DE // AB
\(\Rightarrow\) DE // FB
Tứ giác BFED có:
DE // FB (cmt)
DE = FB (cmt)
\(\Rightarrow BFED\) là hình bình hành
Lời giải:
$DF\parallel AE, DE\parallel AF$ nên $AEDF$ là hình bình hành
$P_{AEDF}=AE+DF+DE+AF$
Lại có:
$DF\parallel AC$ nên áp dụng định lý Talet:
$\frac{DF}{AC}=\frac{BF}{AB}$. Mà $AB=AC$ nên $DF=BF$
$DE\parallel AB$ nên áp dụng định lý Talet:
$\frac{CE}{AC}=\frac{DE}{AB}$ mà $AB=AC$ nên $CE=DE$
Do đó:
$P_{AEDF}=AE+BF+CE+AF=(AE+CE)+(BF+AF)=AC+AB=4+4=8$ (cm)
Hình vẽ:
![](data:image/png;base64,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)