Cho tam giác nhọn ABC (AB<AC) có góc A= 60 độ D là trung điểm của AC . Trên AB lay E sao cho AE=AD . CMR: a) tam giác ADE đều b) tam giác DEC cân c) CE vuông góc AB
Giúp mk cần gấp=>mk tích sao cho......
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19 tháng 8 2021
a: Xét ΔMEN vuông tại E và ΔMFQ vuông tại F có
\(\widehat{FMQ}\) chung
Do đó: ΔMEN\(\sim\)ΔMFQ
b: Ta có: ΔMEN\(\sim\)ΔMFQ
nên \(\dfrac{ME}{MF}=\dfrac{MN}{MQ}\)
hay \(\dfrac{ME}{MN}=\dfrac{MF}{MQ}\)
Xét ΔMEF và ΔMNQ có
\(\dfrac{ME}{MN}=\dfrac{MF}{MQ}\)
\(\widehat{FME}\) chung
Do đó: ΔMEF\(\sim\)ΔMNQ
DX
29 tháng 12 2022
Thi đề phòng sớm sớm zậy :))) Thi xong gửi đề cho tui nhe
Hình tự kẻ :
a.
Xét Tam giác CMI và tam giác AKI có:
AI=CI ( I là trung điểm của AC )
góc CIM = góc AIK ( đối đỉnh )
MI = IK ( K đối xứng M qua I )
=> Tam giác CMI = tam giác AKI ( cgc)
=> Góc CMI = Góc IKA ( 2 góc tương ứng )
=> Góc CMK = góc AKM ( slt )
=> AK // MC => AK // BC
b)
Tam giác ABC có:
M là trung điểm của BC (gt)
I là trung điểm của AC (gt)
=> MI là đường trung bình của tam giác ABC
=>\(MI=\dfrac{1}{2}AB\); MI // AB ( tính chất đường trung bình )
Ta có :
K đối xứng với M qua I (gt)
=> I là trung điểm của KM => \(MI=IK=\dfrac{1}{2}MK\)
Ta lại có :
\(MI=IK=\dfrac{1}{2}MK\left(cmt\right)\Rightarrow MK=2MI\left(1\right)\)
\(MI=\dfrac{1}{2}AB\left(cmt\right)\Rightarrow AB=2MI\left(2\right)\)
Từ 1 và 2 ⇒ AB = MK
Tứ giác ABMK có:
AB = MK (cmt)
MK // AB ( MI // AB )
=> tứ giác ABMK Là hình bình hành
c)
Giả sử tứ giác AMCK là Hình Vuông => AM = MC = CK = AK ( tính chất hình vuông )
Tam giác ABC cân có:
AM là đường trung tuyến ( M là trung điểm của BC )
Mà : AM = MC ( cmt )
\(\Rightarrow AM=MC=\dfrac{1}{2}BC\)
\(\Rightarrow\Delta ABC\) vuông cân tại A
Vậy .....
14 tháng 11 2021
a, Vì I là trung điểm AC và MK nên AMCK là hbh
Do đó AK//CM hay AK//BM và \(AK=BM=MC\) (M là trung điểm BC)
Vậy ABMK là hbh
b, Từ câu a ta có AMCK là hbh
c, Để AMCK là hcn thì \(AM\perp MC\) hay AM là đường cao tam giác ABC hay tam giác ABC cân tại A (AM vừa là đường cao vừa là trung tuyến)
VH
25 tháng 2 2017
S tam giác AMN là :
360 x 1/3 = 120 ( cm2 )
Đ/S : 120 cm2
k mk nha bn
25 tháng 2 2017
S tam giác AMN là :
360 x 1/3 = 120 ( cm2 )
Đ/ S : ............
k mk nha
15 tháng 6 2022
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Hình bạn tự vẽ nhé
a) Vì AE=AD nên tam giác ADE cân tại A ; mà A=60 độ . Vậy tam giác ADE là tam giác đều
b) Tam giác ADE là tam giác đều => AD=DE ; mà AD=DC ( D là trung điểm AC)=> DE=DC=> tam giác DEC cân tại D
c) ADB+BDC=180 độ (kề bù)=>BDC=180-ADB=180-60=120
= DBC=DCB=\(\frac{180-120}{2}\)=30
AEC=ABD+DBC=60+30=90 .Vậy CE vuông góc AB
K mình nhé bạn. Chúc bạn học tốt