AIR MATH

Math Question

Given figure ABDC is a rectangle which of the work shown below most directly verifies analytically that diagonals are congruent ? Slope \( A D=\frac{(1-2)}{(4-(-1))}=\frac{-1}{8}=-\frac{1}{8} \) Slope \( B C=\frac{(-2-5)}{(-2-2)}=\frac{-7}{4}=\frac{7}{4} \) \( A D=\sqrt{(4-(-4))^{2}+(1-2)^{2}}=\sqrt{65} \) \( B C=\sqrt{(-2-2)^{2}+(-2-5)^{2}}=\sqrt{65} \) Midpoint \( A D=\left(\frac{++4}{2}, \frac{2+1}{2}\right)=(0,1.5) \) Midpoint \( B C=\left(\frac{2+-2}{2}, \frac{5+-2}{2}\right)=(0,1.5) \) \( A B=\sqrt{(2-(-4))^{2}+(5-2)^{2}}=\sqrt{45} \) \( B D=\sqrt{(4-2)^{2}+(5-1)^{2}}-\sqrt{20} \) \( C D=\sqrt{(4-(-2))^{2}+(1-(-2))^{2}}=\sqrt{45} \) \( A C=\sqrt{(-2-(-4))^{2}+(-2-2)^{2}}=\sqrt{20} \)

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