a. CD = [tex]\sqrt{13}[/tex], EF = [tex]\sqrt{13}[/tex], CD≅EF
How to find CD & EF ?
If [tex](x_{1}, y_{1})[/tex] & [tex](x_{2}, y_{2})[/tex] are co-ordinates of two points then the distance between this two points = [tex]\sqrt{(x_{2}- x_{1}) ^{2}+ (y_{2}- y_{1} )^{2} }[/tex]
Here, Point C = (0, 4) & Point D = (3, 2)
Then CD = [tex]\sqrt{(3-0)^{2} +(2-4)^{2} }[/tex] = [tex]\sqrt{3^{2} +(-2)^{2} }[/tex] = [tex]\sqrt{9+4}[/tex] = [tex]\sqrt{13}[/tex]
And Point E = (-2, 1) & Point F = (-4, -2)
Then EF = [tex]\sqrt{((-4)-(-2))^{2}+ ((-2)-1)^{2} }[/tex]= [tex]\sqrt{(-2)^{2} +(-3)^{2} }[/tex]= [tex]\sqrt{4+9}[/tex]= [tex]\sqrt{13}[/tex]
Is CD & EF congruent ?
We know that, if two line segment have same length, they are congruent.
Here CD = EF = [tex]\sqrt{13}[/tex]
Since CD & EF have same length, so CD is congruent to EF.
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