Cho tam giác ABC cân tại A có BC = 6cm. Gọi M,N,P lần lượt là trung điểm của AB, AC, BCa) Tính độ dài MN? Chứng minh MBNC là hình thang cânb) Gọi K là điểm đối xứng của B qua N. Chứng minh tứ giác ABCK là hình bình hànhc) Gọi H là điểm đối xứng của P qua M. Chứng minh AHBP là hình chữ nhậtd) Chứng minh AMPN là hình thoia. MN = ?Trong ΔABC có: M là trung điểm AB (gt) N là trung điểm AC (gt)⇒ MN là đường trung bình ΔABC⇒ MN =...
Đọc tiếp
Cho tam giác ABC cân tại A có BC = 6cm. Gọi M,N,P lần lượt là trung điểm của AB, AC, BC
a) Tính độ dài MN? Chứng minh MBNC là hình thang cân
b) Gọi K là điểm đối xứng của B qua N. Chứng minh tứ giác ABCK là hình bình hành
c) Gọi H là điểm đối xứng của P qua M. Chứng minh AHBP là hình chữ nhật
d) Chứng minh AMPN là hình thoi
![](data:image/png;base64,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)
a. MN = ?
Trong ΔABC có:
M là trung điểm AB (gt)
N là trung điểm AC (gt)
⇒ MN là đường trung bình ΔABC
⇒ MN = 1/2BC (t/c)
Mà BC = 6cm (gt)
⇒ MN=BC/2=6/2=3(cm)
C/m: BMNC là hình thang cân
Có MN là đường trung bình ΔABC
⇒ MN//BC
⇒ BMNC là hình thang
Mà góc ABC = góc ACB (ΔABC cân tại A)
⇒ BMNC là hình thang cân (DHNB)
b. C/m: ABCK là hình bình hành
Xét tứ giác ABCK có:
N là trung điểm AC (gt)
N là trung điểm BK (K đ/x với B qua M)
⇒ ABCK là hình bình hành (DHNB)
c. C/m: AHBP là hình chữ nhật
Xét tứ giác AHBP có:
M là trung điểm AB (gt)
M là trung điểm PH ( H đ/x với P qua M)
⇒ AHBP là hình bình hành (DHNB)
Có ΔABC cân tại A
⇒ AP là trung tuyến đồng thời là đg cao
⇒ góc APB = 90 độ
⇒ AHBP là hình chữ nhật (DHNB)
d) Chứng minh AMPN là hình thoi
Tính giúp mình câu d nha!!!
trả lời nhanh giúp mik để mik cho
Tự vẽ hình
a) Vì ABC là tam giác cân => góc B=C (1)
Xét tam giác ABC có
M là tđ AB
N là tđ AC
Suy ra MN là đg tb của ABC
=> MN || BC và BC=2MN (2)
Từ (1) và (2) => MNCB là hình thang cân
b) Vì D đối xứng H qua N => HN=ND=1/2 DH
Xét ADCH có
N là tđ AC
N là tđ DH (cmt)
Suy ra ADCH là hbh (3)
Xét tam giác ABC có
H là tđ BC
ABC cân
Suy ra AH là đường trung trực (tc) => AHC= 90 độ (4)
Từ (3) và(4) => ADCH là hcn
Vì MN || BC và MN=1/2 BC => MN=CH
Mà DA || CH và DA = CH => DA || MN và DA= MN
=> ADMN là hbh
Phần c d đăng sau