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Xét ∆ABC và ∆DBC có: 

AB = BD 

Góc ABC = góc CBD 

Góc BAC = góc BDC 

=> ∆ABC = ∆DBC

xét ΔABC và ΔDBC, ta có :

góc A = góc D (gt)

BC là cạnh chung

góc ABC = góc DBC

=> ΔABC = ΔDBC, (g.c.g)

Bài 3:

a: AC//BD

AC⊥BA

Do đó: BD⊥BA

b: AC//BD

=>\(\hat{ACD}+\hat{CDB}=180^0\) (hai góc trong cùng phía)

=>\(\hat{CDB}=180^0-120^0=60^0\)

c: CI là phân giác của góc ACD

=>\(\hat{ACI}=\hat{DCI}=\frac12\cdot\hat{ACD}=60^0\)

Xét ΔCID có \(\hat{CID}+\hat{DCI}+\hat{CDI}=180^0\)

=>\(\hat{CID}=180^0-60^0-60^0=60^0\)

Câu 37:

a: \(\frac{-7}{15}\cdot\frac{5}{-21}\)

\(=\frac{-7}{-21}\cdot\frac{5}{15}\)

\(=\frac13\cdot\frac13=\frac19\)

b: \(-\frac49:\frac23=-\frac49\cdot\frac32=-\frac{12}{18}=-\frac23\)

c: \(-\frac{3}{15}\cdot\frac{35}{-7}=\frac{3}{15}\cdot\frac{35}{7}=\frac15\cdot5=1\)

d: \(-\frac49:\left(-2\frac23\right)=-\frac49:\frac{-8}{3}=\frac49:\frac83=\frac49\cdot\frac38=\frac{12}{72}=\frac16\)

Câu 36:

a: \(-3,5\cdot\frac{-4}{21}=\frac{-3,5\cdot\left(-4\right)}{21}=\frac{14}{21}=\frac23\)

b: \(1\frac23\cdot\left(-2\frac13\right)=-\frac53\cdot\frac73=-\frac{35}{9}\)

c: \(\left(-2,5\right):\frac{3}{-4}=\left(-2,5\right)\cdot\frac{\left(-4\right)}{3}=\frac{10}{3}\)

d: \(\left(-8\frac25\right):\left(-2\frac45\right)=\frac{-42}{5}:\frac{-14}{5}=\frac{42}{14}=3\)

Câu 35:

a: \(\frac32\cdot\frac{-2}{25}=\frac{3}{25}\cdot\frac{-2}{2}=-\frac{3}{25}\)

b: \(\frac{-8}{5}\cdot\frac{-3}{4}=\frac85\cdot\frac34=\frac{24}{20}=\frac65\)

c: \(-\frac{15}{4}:\frac{-21}{10}=\frac{15}{4}:\frac{21}{10}=\frac{15}{4}\cdot\frac{10}{21}=\frac{10}{4}\cdot\frac{15}{21}=\frac52\cdot\frac57=\frac{25}{14}\)

d: \(-\frac{15}{7}:\frac{5}{14}=-\frac{15}{7}\cdot\frac{14}{5}=\frac{-210}{35}=-6\)

Câu 34:

\(-3\frac15\cdot2,5=-\frac{16}{5}\cdot\frac52=-\frac{16}{2}=-8\)

Câu 33:

a: \(\frac{-1}{21}+\frac{-1}{14}=\frac{-2}{42}+\frac{-3}{42}=\frac{-2-3}{42}=-\frac{5}{42}\)

b: \(\frac{-3}{7}+\frac{-2}{9}=\frac{-27}{63}+\frac{-14}{63}=-\frac{27+14}{63}=-\frac{41}{63}\)

c: \(\frac{-5}{12}+\frac{7}{18}=-\frac{15}{36}+\frac{14}{36}=\frac{-15+14}{36}=\frac{-1}{36}\)

d: \(\frac{-4}{15}+0,75=-\frac{4}{15}+\frac34=-\frac{16}{60}+\frac{45}{60}=\frac{45-16}{60}=\frac{29}{60}\)

e: \(-\frac23+1,1=-\frac23+\frac{11}{10}=-\frac{20}{30}+\frac{33}{30}=\frac{33-20}{30}=\frac{13}{30}\)

f: \(-3\frac12-4\frac14=-\frac72-\frac{17}{4}=\frac{-14}{4}-\frac{17}{4}=-\frac{31}{4}\)

Câu 32:

a: \(\frac{1}{12}+\frac{-3}{12}=\frac{1-3}{12}=-\frac{2}{12}=-\frac16\)

b: \(\frac78-\frac54=\frac78-\frac{10}{8}=\frac{7-10}{8}=-\frac38\)

c: \(1\frac25+3\frac35=1+\frac25+3+\frac35=4+1=5\)

d: \(\frac{-14}{20}+0,6=-\frac{14}{20}+\frac{12}{20}=-\frac{2}{20}=-\frac{1}{10}\)

Câu 31:

\(A=-\frac15+\frac{8}{15}\)

\(=-\frac{3}{15}+\frac{8}{15}=\frac{5}{15}=\frac13\)

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