3.14:

Ta thấy $\widehat{xNM}=\widehat{xQP}=45^0$. Mà 2 góc này ở vị trí đồng vị nên $MN\parallel PQ$

3.15

$EF\parallel NP$ do cùng vuông góc với $MH$

3.16: Bạn tự vẽ hình nhé.

3.17:

Ta thấy $\widehat{yKH}+\widehat{KHx}=130^0+50^0=180^0$. Mà 2 góc này ở vị trí trong cùng phía nên $Ky\parallel Hx$

Bài 6 : 

\(n_{Fe}=\dfrac{5,6}{56}=0,1\left(mol\right)\)

Pt : \(Fe+2HCl\rightarrow FeCl_2+H_2|\)

       1          2             1           1

     0,1                       0,1        0,1

a) \(n_{H2}=\dfrac{0,1.1}{1}=0,1\left(mol\right)\)

\(V_{H2\left(dktc\right)}=0,1.22,4=2,24\left(l\right)\)

b) \(n_{FeCl2}=\dfrac{0,1.1}{1}=0,1\left(mol\right)\)

⇒ \(m_{FeCl2}=0,1.127=12,7\left(g\right)\)

 Chúc bạn học tốt

a, Xét tg ADH và tg BCK có 

\(AD=BC;\widehat{ADH}=\widehat{BCK}\) (hình thang cân ABCD)\(;\widehat{AHD}=\widehat{BKC}\left(=90^0\right)\)

Nên \(\Delta ADH=\Delta BCK\left(ch-gn\right)\)

\(\Rightarrow DH=CK\)

3.15:
EF vuông góc MH

NP vuông góc MH

Do đó: EF//NP

3.17:

góc yKH+góc H=180 độ

mà hai góc này là hai góc ở vị trí trong cùng phía

nên Ky//Hx

a) ĐKXĐ: \(\left\{{}\begin{matrix}x\le-1\\x\ge2\end{matrix}\right.\)

\(\sqrt{x^2-x-2}-\sqrt{x-2}=0\\ \Leftrightarrow\sqrt{x^2-x-2}=\sqrt{x-2}\\ \Leftrightarrow x^2-x-2=x-2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)

\(a,ĐK:x\ge2\\ PT\Leftrightarrow x^2-x-2=x-2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=0\left(ktm\right)\end{matrix}\right.\Leftrightarrow x=2\\ b,ĐK:\left[{}\begin{matrix}x\le-1\\x\ge1\end{matrix}\right.\\ PT\Leftrightarrow\sqrt{x^2-1}=x^2-1\\ \Leftrightarrow x^2-1=\left(x^2-1\right)^2\\ \Leftrightarrow\left(x^2-1\right)\left(x^2-1-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-1\left(tm\right)\\x=\sqrt{2}\left(tm\right)\\x=-\sqrt{2}\left(tm\right)\end{matrix}\right.\)

\(c,ĐK:\left[{}\begin{matrix}x\le-2\\x\ge1\end{matrix}\right.\\ PT\Leftrightarrow\sqrt{x^2-x}=-\sqrt{x^2+x-2}\\ \Leftrightarrow x^2-x=x^2+x-2\\ \Leftrightarrow2x=2\\ \Leftrightarrow x=1\left(tm\right)\)

\(d,ĐK:x\ge1\\ PT\Leftrightarrow\sqrt{\left(x^2-1\right)^2}=x-1\\ \Leftrightarrow\left|x^2-1\right|=x-1\\ \Leftrightarrow\left[{}\begin{matrix}x^2-1=x-1\left(x\le-1;x\ge1\right)\\x^2-1=1-x\left(-1< x< 1\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\left(tm\right)\\x=1\left(tm\right)\end{matrix}\right.\\\left[{}\begin{matrix}x=1\left(ktm\right)\\x=-2\left(ktm\right)\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

\(e,PT\Leftrightarrow\left|x+2\right|+\left|x-4\right|=0\Leftrightarrow\left\{{}\begin{matrix}x+2=0\\x-4=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=-2\\x=4\end{matrix}\right.\Leftrightarrow x\in\varnothing\)

\(g,\Leftrightarrow x\in\varnothing\left(\sqrt{x-2}+\sqrt{x-3}\ge0>-5\right)\\ f,\Leftrightarrow\left|x-1\right|+\left|x-3\right|=1\\ \Leftrightarrow\left[{}\begin{matrix}1-x+3-x=1\left(x< 1\right)\\x-1+3-x=1\left(1\le x< 3\right)\\x-1+x-3=1\left(x\ge3\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\left(ktm\right)\\0x=-1\left(ktm\right)\\x=\dfrac{5}{2}\left(ktm\right)\end{matrix}\right.\\ \Leftrightarrow x\in\varnothing\)

\(BC=\sqrt{8^2+5^2}=\sqrt{89}\approx9,4\left(cm\right)\)

Bài 5: 

a: Xét ΔBEC và ΔADC có 

\(\widehat{C}\) chung

\(\widehat{EBC}=\widehat{DAC}\)

Do đó: ΔBEC\(\sim\)ΔADC

tk: