Question Number 185869 by Mingma last updated on 29/Jan/23
![](https://www.tinkutara.com/question/28921.png)
Answered by mr W last updated on 29/Jan/23
![](https://www.tinkutara.com/question/28928.png)
Commented by mr W last updated on 29/Jan/23
![75°+60°+45°=180° ⇒D,E,F are collinear!](https://www.tinkutara.com/question/Q185878.png)
$$\mathrm{75}°+\mathrm{60}°+\mathrm{45}°=\mathrm{180}° \\ $$$$\Rightarrow{D},{E},{F}\:{are}\:{collinear}! \\ $$
Answered by ajfour last updated on 29/Jan/23
![E((a/2), ((a(√3))/2)) F(a+((a(√3))/2) , (a/2)) D(0,a) slope of EF=−((((√3)−1)/( (√3)+1))) slope of DE=−(2−(√3)) and they are equal!](https://www.tinkutara.com/question/Q185881.png)
$${E}\left(\frac{{a}}{\mathrm{2}},\:\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\:\:\:\:{F}\left({a}+\frac{{a}\sqrt{\mathrm{3}}}{\mathrm{2}}\:,\:\frac{{a}}{\mathrm{2}}\right)\:\:{D}\left(\mathrm{0},{a}\right) \\ $$$${slope}\:{of}\:{EF}=−\left(\frac{\sqrt{\mathrm{3}}−\mathrm{1}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\right) \\ $$$${slope}\:{of}\:{DE}=−\left(\mathrm{2}−\sqrt{\mathrm{3}}\right) \\ $$$${and}\:{they}\:{are}\:{equal}! \\ $$