Cho ▲ABC nhọn <A bằng 60o Chứng minh BC2=AB2 + AC2 -AB.AC
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Hạ đường cao AH của △ABC
⇒AH⊥BC
Vì △ABC nhọn
⇒Điểm H nằm giữa 2 điểm B và C
Diện tích △ABC là: SABC=\(\dfrac{1}{2}\).BC.AH(1)
Áp dụng hệ thức giữa cạnh và góc vào △AHB(H=900 ),ta có:
AH=AB.\(\sin B\)(2)
Từ (1) và (2)⇒SABC=BC.AB.\(\sin B\)(đpcm)
Bài 1:
Kẻ đường cao $AH$ của tam giác $ABC$. Ta có:
\(\sin A=\frac{BH}{AB}\)
Mà \(\frac{1}{2}BH.AC=S_{ABC}\Rightarrow BH=\frac{2S_{ABC}}{AC}\)
\(\Rightarrow \sin A=\frac{2S_{ABC}}{AB.AC}\)
\(\Rightarrow \frac{BC}{\sin A}=\frac{AB.AC.BC}{2_{ABC}}\)
Hoàn toàn tương tự, kẻ đường cao từ đỉnh $B,C$ , cuối cùng ta có:
\(\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}=\frac{AB.BC.AC}{2S_{ABC}}\)
Vậy ta có đpcm.
cho tam giác ABC nhọn (AB<AC) nội tiếp đường tròn (O;K) có BD là đường kính và đường cao AH của tam giác ABC cắt (O;K) tại E đề nek
đề đây nha mn :(( cho tam giác ABC nhọn (AB<AC) nội tiếp đường tròn (O;K) có BD là đường kính và đường cao AH của tam giác ABC cắt (O;K) tại E
Cho tam giác ABC nhọn AB<AC M là trung điểm của BC trên tia đời của tia MA có điểm E s cho AM=ME
a) cmr tam giác AMB=CMR
b từ A kẻ D s cho HA =HD cmr CE = BP
c cmr CE = CD tam giác AMD là tam giác j vì s
D CMR AM NHỎ HƠN AB +AC /2
CHỈ LM MỖI Ý D THUI NHA NHANH NHA
a: Xét ΔAMB và ΔEMC có
MA=ME
góc AMB=góc EMC
MB=MC
=>ΔAMB=ΔEMC
b: Xet ΔBAD có
BH vừa là đường cao, vừa là trung tuyến
=>ΔBAD cân tại B
=>BD=BA=CE
c: Xet ΔMAD có
MH vừa là đường cao,vừa là trung tuyến
=>ΔMAD cân tại M
d: AM<1/2(AB+AC)
=>AE<AB+AC
=>AE<BE+AB(luôn đúng)
Xét ΔABC có \(cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}=\dfrac{1}{2}\)
\(\Leftrightarrow AB^2+AC^2-BC^2=AB\cdot AC\)
hay \(BC^2=BA^2+AC^2-AB\cdot AC\)