a:

Sửa đề; Chứng minh ΔOQM đều

Xét tứ giác DEBC có DE//BC và \(\hat{DBC}=\hat{ECB}\left(=60^0\right)\)

nên DEBC là hình thang cân

Ta có: OQ//AB

=>\(\hat{OQM}=\hat{ABC}\) (hai góc đồng vị)

=>\(\hat{OQM}=60^0\)

OM//AC
=>\(\hat{OMQ}=\hat{ACB}\) (hai góc đồng vị)

=>\(\hat{OMQ}=60^0\)

Xét ΔOMQ có \(\hat{OQM}=\hat{OMQ}\left(=60^0\right)\)

nên ΔOMQ đều

b: DE//BC

=>\(\hat{ODN}=\hat{ABC}\) (hai góc đồng vị)

=>\(\hat{ODN}=60^0\)

DO//BC

=>\(\hat{NOD}=\hat{OMQ}\) (hai góc đồng vị)

=>\(\hat{NOD}=60^0\)

Xét ΔOND có \(\hat{ODN}=\hat{NOD}=60^0\)

nên ΔOND đều

Ta có: DE//BC

=>\(\hat{OEP}=\hat{ACB}\) (hai góc đồng vị)

=>\(\hat{OEP}=60^0\)

OE//QC

=>\(\hat{POE}=\hat{PQC}\) (hai góc đồng vị)

=>\(\hat{POE}=60^0\)

Xét ΔOPE có \(\hat{OEP}=\hat{POE}=60^0\)

nên ΔOPE đều

ΔOQM đều

mà OI là đường cao

nên I là trung điểm của QM

ΔODN đều

mà OH là đường cao

nên H là trung điểm của DN

ΔOPE cân tại O

mà OK là đường cao

nên K là trung điểm của PE

Xét tứ giác BDOQ có

BD//OQ

BQ//DO

Do đó: BDOQ là hình bình hành

Xét tứ giác CEOM có

CE//OM

CM//OE

Do đó: CEOM là hình bình hành

AH+BI+CK

=AN+NH+BQ+QI+CE+EK

=AN+1/2ND+BQ+1/2QM+CE+1/2EP

=AN+1/2OD+BQ+1/2OQ+CE+1/2OE

=AN+BQ+CE+1/2DE+1/2BD

=AN+BQ+CE+1/2AD+1/2BD

=AN+BQ+CE+1/2AB

=AN+DO+OM+1/2AB

=AN+ND+OQ+1/2AB

=AD+BD+1/2AB

=AB+1/2AB

=1,5AB=1,5a

a: Xét ΔBAE vuông tại A và ΔCAD vuông tại A có

BA=CA

AE=AD

Do đó: ΔBAE=ΔCAD

b: Ta có: \(\hat{ABE}+\hat{KDB}=90^0\) (KD⊥BE)

\(\hat{AMD}+\hat{ADM}=90^0\) (ΔADM vuông tại A)

mà \(\hat{KDB}=\hat{MDA}\) (hai góc đối đỉnh)

nên \(\hat{ABE}=\hat{AMD}\)

mà \(\hat{ABE}=\hat{ACD}\)

nên \(\hat{AMD}=\hat{ACD}\)

=>ΔDCM cân tại D

c: ΔDCM cân tại D

mà DA là đường cao

nên A là trung điểm của CM

Xét ΔCMK có

A là trung điêm của CM

AH//MK

Do đó: H là trung điểm của CK

=>CH=HK

GIÚP MÌNH VỚI CÁC BẠN ƠI!!!

ARIGATO!!!

Tham khảo ở đây nha

https://olm.vn/hoi-dap/detail/12435070952.html

Tham khảo ở đây nha

Câu hỏi của Phạm Hương Giang - Toán lớp 7 - Học toán với OnlineMath

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