Cho Tam giác ABC (C<45 độ) AB=c ; BC=a ; AC=b đường cao AH=h trung tuyến AM=m
CMR \(1-c\text{os}2\alpha=2sin^2\alpha\)
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a) Tam giác ABC nhọn:
b) Tam giác ABC vuông tại A:
c) Tam giác ABC có góc A tù:
a: Xét ΔABC có AB=AC
nên ΔABC cân tại A
=>\(\widehat{ABC}=\widehat{ACB}\)
b: Ta có: ΔABC cân tại A
=>\(\widehat{ABC}=\widehat{ACB}\)
mà \(\widehat{ABC}=70^0\)
nên \(\widehat{ACB}=70^0\)
Ta có: ΔABC cân tại A
=>\(\widehat{BAC}=180^0-2\cdot\widehat{B}=40^0\)
c: Sửa đề: Chứng minh ΔABI=ΔACI
Xét ΔABI và ΔACI có
AB=AC
BI=CI
AI chung
Do đó: ΔABI=ΔACI
d: Xét tứ giác ABMC có
I là trung điểm chung của AM và BC
=>ABMC là hình bình hành
=>MB=AC và MB//AC
e: Xét tứ giác ANBM có
K là trung điểm chung của AB và MN
=>ANBM là hình bình hành
=>AN//BM và AN=BM
Ta có: AN//BM
AC//BM
AN,AC có điểm chung là A
Do đó: N,A,C thẳng hàng
Ta có: AN=BM
AC=BM
Do đó: AN=AC
mà N,A,C thẳng hàng
nên A là trung điểm của NC
a: Xét ΔAIB và ΔEIC có
IB=IC
\(\widehat{AIB}=\widehat{EIC}\)
IA=IE
Do đó: ΔAIB=ΔEIC
b: Xét ΔABC và ΔECB có
AB=EC
\(\widehat{ABC}=\widehat{ECB}\)
BC chung
Do đó: ΔABC=ΔECB
a: Xét ΔABC có \(BC^2=AB^2+AC^2\)
nên ΔABC vuông tại A
b: \(BM=\sqrt{AB^2+AM^2}=25\left(cm\right)\)
CM=AC-AM=25(cm)
Xét ΔBMC có MB=MC
nên ΔMBC cân tại M
c: \(\widehat{ABC}=50^0\)