Chứng minh HM=AMcap H cap M equals cap A cap M
𝐻𝑀=𝐴𝑀
Mcap M
𝑀
là trung điểm của ACcap A cap C
𝐴𝐶
, suy ra AM=MC=AC2=42=2 cmcap A cap M equals cap M cap C equals the fraction with numerator cap A cap C and denominator 2 end-fraction equals 4 over 2 end-fraction equals 2 cm
𝐴𝑀=𝑀𝐶=𝐴𝐶2=42=2 cm
.
Trong tam giác vuông AHCcap A cap H cap C
𝐴𝐻𝐶
, HMcap H cap M
𝐻𝑀
là đường trung tuyến ứng với cạnh huyền ACcap A cap C
𝐴𝐶
.
Đường trung tuyến ứng với cạnh huyền trong tam giác vuông bằng một nửa cạnh huyền, do đó HM=AC2=42=2 cmcap H cap M equals the fraction with numerator cap A cap C and denominator 2 end-fraction equals 4 over 2 end-fraction equals 2 cm
𝐻𝑀=𝐴𝐶2=42=2 cm
.
Từ đó, HM=AM=2 cmcap H cap M equals cap A cap M equals 2 cm
𝐻𝑀=𝐴𝑀=2 cm
được chứng minh.
Chứng minh tam giác AHMcap A cap H cap M
𝐴𝐻𝑀
đều
Đã chứng minh AM=HM=2 cmcap A cap M equals cap H cap M equals 2 cm
𝐴𝑀=𝐻𝑀=2 cm
.
Theo giả thiết, AH=2 cmcap A cap H equals 2 cm
𝐴𝐻=2 cm
.
Vì AH=AM=HM=2 cmcap A cap H equals cap A cap M equals cap H cap M equals 2 cm
𝐴𝐻=𝐴𝑀=𝐻𝑀=2 cm
, tam giác AHMcap A cap H cap M
𝐴𝐻𝑀
là tam giác đều.
 
Tính số đo góc Dcap D
𝐷
Trong tam giác đều AHMcap A cap H cap M
𝐴𝐻𝑀
, góc HAM=60∘cap H cap A cap M equals 60 raised to the exponent composed with end-exponent
𝐻𝐴𝑀=60∘
.
Trong hình thoi ABCDcap A cap B cap C cap D
𝐴𝐵𝐶𝐷
, ACcap A cap C
𝐴𝐶
là đường chéo.
Góc DACcap D cap A cap C
𝐷𝐴𝐶
bằng góc HAMcap H cap A cap M
𝐻𝐴𝑀
, suy ra góc DAC=60∘cap D cap A cap C equals 60 raised to the exponent composed with end-exponent
𝐷𝐴𝐶=60∘
.
Trong hình thoi, đường chéo là đường phân giác của góc.
Do đó, góc DAB=2⋅góc DAC=2⋅60∘=120∘cap D cap A cap B equals 2 center dot góc cap D cap A cap C equals 2 center dot 60 raised to the exponent composed with end-exponent equals 120 raised to the exponent composed with end-exponent
𝐷𝐴𝐵=2⋅góc 𝐷𝐴𝐶=2⋅60∘=120∘
.
Trong hình thoi, các góc đối bằng nhau, suy ra góc BCD=góc DAB=120∘cap B cap C cap D equals góc cap D cap A cap B equals 120 raised to the exponent composed with end-exponent
𝐵𝐶𝐷=góc 𝐷𝐴𝐵=120∘
.
Tổng các góc trong hình thoi là 360∘360 raised to the exponent composed with end-exponent
360∘
.
Góc D+góc B=360∘−(góc DAB+góc BCD)=360∘−(120∘+120∘)=360∘−240∘=120∘cap D plus góc cap B equals 360 raised to the exponent composed with end-exponent minus open paren góc cap D cap A cap B plus góc cap B cap C cap D close paren equals 360 raised to the exponent composed with end-exponent minus open paren 120 raised to the exponent composed with end-exponent plus 120 raised to the exponent composed with end-exponent close paren equals 360 raised to the exponent composed with end-exponent minus 240 raised to the exponent composed with end-exponent equals 120 raised to the exponent composed with end-exponent
𝐷+góc 𝐵=360∘−(góc 𝐷𝐴𝐵+góc 𝐵𝐶𝐷)=360∘−(120∘+120∘)=360∘−240∘=120∘
.
Vì góc D=góc Bcap D equals góc cap B
𝐷=góc 𝐵
, suy ra góc D=120∘2=60∘cap D equals the fraction with numerator 120 raised to the exponent composed with end-exponent and denominator 2 end-fraction equals 60 raised to the exponent composed with end-exponent
𝐷=120∘2=60∘
.
 
Tính các góc của hình thoi ABCDcap A cap B cap C cap D
𝐴𝐵𝐶𝐷
Các góc của hình thoi ABCDcap A cap B cap C cap D
𝐴𝐵𝐶𝐷
là:
Góc DAB=120∘cap D cap A cap B equals 120 raised to the exponent composed with end-exponent
𝐷𝐴𝐵=120∘
.
Góc BCD=120∘cap B cap C cap D equals 120 raised to the exponent composed with end-exponent
𝐵𝐶𝐷=120∘
.
Góc ADC=60∘cap A cap D cap C equals 60 raised to the exponent composed with end-exponent
𝐴𝐷𝐶=60∘
.
Góc ABC=60∘cap A cap B cap C equals 60 raised to the exponent composed with end-exponent
𝐴𝐵𝐶=60∘
.
 
Kết quả cuối cùng
HM=AM=2 cmcap H cap M equals cap A cap M equals 2 cm
𝐻𝑀=𝐴𝑀=2 cm
.
Tam giác AHMcap A cap H cap M
𝐴𝐻𝑀
là tam giác đều.
Góc D=60∘cap D equals 60 raised to the exponent composed with end-exponent
𝐷=60∘
.
Các góc của hình thoi ABCDcap A cap B cap C cap D
𝐴𝐵𝐶𝐷
là: góc DAB=120∘góc cap D cap A cap B equals 120 raised to the exponent composed with end-exponent
góc 𝐷𝐴𝐵=120∘
, góc BCD=120∘góc cap B cap C cap D equals 120 raised to the exponent composed with end-exponent
góc 𝐵𝐶𝐷=120∘
, góc ADC=60∘góc cap A cap D cap C equals 60 raised to the exponent composed with end-exponent
góc 𝐴𝐷𝐶=60∘
, góc ABC=60∘góc cap A cap B cap C equals 60 raised to the exponent composed with end-exponent
góc 𝐴𝐵𝐶=60∘
.